The old city center or Centro Historico of Mexico City, centered around the Plaza de la Constitucion, commonly known as Zócalo, is an area clearly different from the rest of the city for its Colonial and European architecture and narrow cobblestone streets. It has an enormous amount of stores, street vendors, and specially crowds. Without doubt, this area is the most touristy not only in the city but probably in the country, a place with the taste of the Mexico people have in their minds for its architecture, food and most importantly its people. For good or bad, this is the place where rich and poor, old and new, cheap and expensive, beautiful and disgusting meet.
The Centro Historico, the original foundation of Mexico City, was built on the ruins of Tenochtitlan, the Aztec empire capital established around 1325 and destroyed by the Spanish in 1521. It contains a large collection of old buildings that date back to the 16th century. Because of its importance, it was included in UNESCO's list of world heritage places in 1987.
WARNING: On Sundays, several streets of the Centro are closed for motor vehicles due to "bike" day (confined streets for bicycle use only). It is strongly advised to avoid driving these days. If you are staying at any of the hotels in this area and have a flight scheduled on sunday, it is advised to allow enough time to get out of the area if you're using a Taxi. An alternative to get in and out of the area is the Metro (Subway)
This is probably the best way to reach the Centro Historico, however, all the stations in the area are very crowded around the clock, so prepare to be crushed iniside cars and be also careful of pickpockets.
There are various Metro lines that connect the Centro Historico with the rest of the City.
Line 1 (pink) Pino Suarez, Isabel La Catolica and Salto del Agua Stations
Line 2 (blue) Zocalo (your best choice for direct access), Allende, Bellas Artes, Hidalgo and Revolucion stations
Line 3 (green) Hidalgo and Juarez stations
The hop-in hop-off double-decker bus makes a stop just north of the Zocalo in Monte de Piedad street in the west side of the Cathedral. The one-day pass costs $120 pesos.
By Public Bus
The RTP bus network rides along Eje Central Avenue. You may also ride a Microbus.
By Trolley Bus
The Trolley Bus rides along Eje Central Avenue. Ask the driver to drop you off at Madero street.
This is the least recommended way to get around Centro Historico since the streets are always jammed with hundreds of cars specially during weekdays.
If you dare to enter the area by car, you can do so through Reforma and turning right at Avenida Juarez which later becomes Francisco I Madero Street, or if you're coming from the south, you can reach through Calzada de Tlalpan which later becomes 20 de Noviembre Avenue.
There are several parking lots in the area (valet service) that charge $14.00 pesos an hour.
The best way to get around the Centro Historico is definitely by foot. All tourist attractions are within walking distance.
By Tourist Trolley
This trolley (in spanish Tranvia) departs from Juarez Avenue 66, between the Alameda and the Palacio de Bellas Artes. Ride lasts 45 minutes around many interesting spots in the area. Operating hours Monday thru Sunday 10:00 to 17:00
There are a few pedicabs that can carry you within the Centro Historico.
Palacio de Bellas Artes
Old City Hall with Independence Celebration decoration
Banco de Mexico building
Palacio Postal (indoors)
Plaza de la Constitucion or Zocalo This square comprises 57,200 square meters and is one of the largest squares in the world. It boasts a huge mexican flag in the center.
Palacio Nacional Located in Plaza de la Constitucion (Zocalo), this palace is the office of the President of Mexico, its construction started in 1693 and served as the Palace of the Viceroy of the New Spain. The walls inside the palace contain paintings by Diego Rivera that describe the history of Mexico from the pre-columbian age to the mexican revolution. You can also visit the Recinto Legislativo, office of the first Mexican Congress, and recinct homage to Benito Juarez. Free entrance.
Cathedral Plaza de la Constitucion (Zocalo). The largest cathedral in the American continent. Its construction started in 1573 according to the design plans of Claudio de Arcinieaga and its construction lasted for more than 300 years.
Sagrario Metropolitano A side chapel next to the Cathedral completed in 1769.
Nacional Monte de Piedad. Monte de Piedad and Cinco de Mayo. This building completed in 1758 was built on the grounds of the house of Aztec emperor Moctezuma and later the residence of the spanish conqueror Hernan Cortes. The building was acquired in 1838 by Nacional Monte de Piedad, a pawn shop established in 1775 that still operates today. Monday-Friday 8:30-18:00; Saturday 8:30-15:30, Sundays closed.
City Hall Plaza de la Constitucion (Zocalo)
Aztec Ruins of Templo Mayor Seminario 8
Plaza Manuel Gamio Seminario between Moneda and Guatemala streets. Features a open-air diorama of the old Tenochtitlan.
Latinoamericana Tower Eje Central Avenue and Francisco I Madero Street. Construction started in 1948 and was completed in 1956, this was Mexico's first skyscraper, boasting 44 floors and 182 meters. There is an observatory in the 42nd floor, entrance is $50 pesos. Working hours Monday thru Sunday 9:00 to 22:00.
Palacio de Bellas Artes Juarez Avenue and Eje Central. Designed by Italian architect Adamo Boari. Its construction started in 1905, however due to the Revolution War it was completed until 1934.
Plaza Manuel Tolsa Tacuba 8. In this beautiful square you can find the Palacio de Mineria,National Art Museum and the statue of spanish king Charles IV also known as "El Caballito" (the little horse).
Palacio de Mineria Tacuba 5. Formerly the Mining College, this building, dated 1792 features an old library and a chapel. It serves as venue for the yearly Mexico City Book Fair.
Templo de San Francisco Francisco I Madero 7. This church was started in the 16th century and completed in the 19th century. This temple was built in the grounds of the Zoo of Aztec Emperor Moctezuma.
Templo de Felipe de Jesus Francisco I Madero 9. Built in 1897 in the grounds of the former Vasque Church of Aranzazu.
Palacio de Iturbide Francisco I Madero 17. One of the oldest buildings in town, built in the late 16th century, it was first home to the local nobility and later the residence of Mexican Emperor Agustin de Iturbide. The building is owned today by the Cultural Trust of Banco Nacional de Mexico, the mexican branch of Citibank.
Banco de Mexico building Cinco de Mayo and Eje Central Avenue. Office of the Mexican Central Bank built in 1925.
Postal Palace Eje Central Avenue and Tacuba. One of the most beautiful buildings in the country considered national heritage. Built in 1906, this european style building houses the main post office. Most of the materials used to build it were brought from Italy. The best place to send postcards back home. Open Monday-Friday 8:00 to 20:00 , Saturday-Sunday 8:00 to 16:00
Casa de los Azulejos Francisco I Madero 4. This department store and restaurant is housed in the former residency of the Counts of the Valley of Orizaba. Built ca. 1737. It features tiles made in Puebla It was later conditioned to become the Jockey Club. In the late 19th century it became the Sanborns store, founded by the Sanborn brothers, American immigrants in Mexico City.
Plaza de Santo Domingo Located between the streets of Republica de Cuba, Brasil and Belisario Dominguez, is the second largest square in Centro Historico after the Zocalo. It is surrounded by various important buildings such as the Palacio de la Inquisicion, Santo Domingo convent and the old Customs House.,\
Suprema Corte de Justicia Pino Suarez and Corregidora streets. This building was completed in 1945 designed by architect Antonio Muñoz Garcia.
Plaza de la Fundacion Pino Suarez and Venustiano Carranza streets. This place is allegedly where the Aztecs found the eagle eating a snake on top of a cactus (nopal), the divine sign of the gods to settle down and establish the city of Tenochtitlan. It features a sculpture by Juan Olaguibel made in 1970.
Santa Teresa church Licenciado Verdad 6. Originally built in 1678 and refurbished in 1845.
Customs House located in Plaza de Santo Domingo
Teatro de la Ciudad
Asamblea Legislativa del Distrito Federal
Antiguo Palacio de la Inquisicion Republica de Brasil 33. Built between 1732 and 1737. It was the head office of the Holly Inquisition, the religious authority famous for torturing heretic people. Today houses the Museum of Mexican Medicine.
Nuestra Señora de Loreto
China Town in Dolores street. Recently re-aconditioned this street became a pedestrian-only street full of chinese restaurants and stores.
Gran Hotel de la Ciudad de Mexico Plaza de la Constitucion (Zocalo). Also known as "Centro Mercantil" this building built in 1899 was once a fancy shopping center. It was converted into a hotel in 1966. The lobby of this place was featured in the film "Frida".
Plaza de las Tres Culturas in Tlatelolco, near Centro Historico, shows a mixture of pre-columbian, colonial and modern architecture. To reach this place you need to take a Taxi or the Metro, station Tlatelolco (Line 3, green)
Museo Nacional de Arte)
Mexico City prides itself in having the largest number of museums in the world, and most of these museums are located in Centro Historico. Really worth to see are the Museo Nacional de Arte, Museo del Templo Mayor and Museo Franz Mayer. Remember most museums are closed on Mondays.
Museo Nacional de Arte Tacuba 8. Housed in the former Palace of Telecommunications, this beautiful porfirian-style building was built in 1904 by architect Silvio Contri. The museum presents a permanent collection of early mexican paintings as well as other temporary exhibits. Opening hours: Tuesday-Sunday 10:00-17:30. Entrance $30 pesos.
Museo Franz Mayer Housed in a 18th century building, houses the largest and finest collection of decorative arts in Mexico. The collection, including objects from Mexico, Europe and Asia ranging from the 16th to the 19th century was a donation of German-Mexican philantropist Franz Mayer.
Museo del Templo Mayor Seminario 8. Presents some archaeological findings of the ancient Aztec city of Tenochtitlan.
Museo Postal Eje Central and Tacuba. Housed in the Postal Palace, features old postal stationery and mail boxes.
Museo de la Secretaria de Hacienda Moneda 4. (Former Palace of the Archbishop)Built in 1720.
Museo Nacional de las Culturas Moneda 13. Opening hours Tuesday-Saturday 9:30 to 18:00. Housed in the former Mint building built in 1734. The museum is dedicated to antropology of the world.
Museo Jose Luis Cuevas Academia 23. Opening hours Tuesday-Sunday 10:00 to 18:00 Housed in the former convent of Santa Ines built in 1600. The museum's collection features works by Mexican artist Jose Luis Cuevas and also presents some works from Picasso and Rembrandt.
Museo Nacional de San Carlos Academia 22. Housed in a building dated 1785 originally conceived as the former Royal Academy of Beaux Arts. It is administered by the National University and features permanent and temporary painting collections.
Museo Mural Diego Rivera Puente de Alvarado 50. Permanent and temporary exhibits. Features paintings by Diego Rivera.
Museo Nacional de la Estampa Hidalgo Av. 39
Centro Cultural de España Guatemala 18. This is the official cultural center from the Spanish Embassy and features temporary exhibits.
Museo de San Ildefonso Justo Sierra 16 . Managed by the National University, this museum features a great permanent paintings collection and shows important temporary exhibits.
Museo del Estanquillo One of the newest museums in the city.
Museo de la Ciudad de Mexico Pino Suarez 30. Presenting history of the city.
Museo de la Caricatura Donceles 99. Presenting history of Mexican Cartoons (political and amusing cartoons)
Museo de la Luz El Carmen 31 corner with San Ildefonso. Managed by the National University this museum is mostly for students on everything to do with light (photography, electricity, vision, etc)
Museo de la Medicina Mexicana Republica de Brasil 33. Housed in the Inquisition Palace, this museum, managed by the Medicine Faculty of the National University shows history of health care in Mexico since the 19th century. Features a great replica of an old pharmacy.
Museo de la Indumentaria Mexicana Izazaga and 5 de Febrero. Collection of traditional Mexican clothing.
Museo de la Charreria Izazaga 89 (near Isabel La Catrolica. This museum features everything about the Mexican Cowboy, known as Charro.
Beer Museum Bolivar Street 18. Sponsored by Grupo Modelo, brewer of Corona Beer. Open Monday-Thursday 13:00-20:00 Saturday-Friday 13:00-20:00
Museo del Calzado (Shoe Museum). Bolivar 27, 1st Floor. Private collection of old shoes from the 18th, 19th and 20th century. The museum belongs to the shoe store "El Borcegui", established in 1865 and still selling shoes today.
Museo Nacional de la Estampa. Hidalgo 39. Features a collection of old engravings and other graphic arts.
Museo Serfin Madero 33. Housed in the building known as Casa Borda.
Liverpool Department Store
Palacio de Hierro Department Store
La Ideal Bakery
Sanborns (Casa Boker)
Until the 1950's, the Centro Historico was the main shopping district of the City. Many of the prestigious department stores of the country such as Liverpool and El Palacio de Hierro opened their first stores here. Today, the area is still one of the busiest shopping areas of the city. The area has several streets dedicated to a particular kind of shopping, something inherited from the Spanish. Shopping in the Centro Historico is a real back-in-time experience as many of the spaces where the stores are located are truly historical.
Republica del Salvador Street The first half of the street (from Eje Central Avenue to Isabel La Catolica Avenue) specializes in all sorts of electronics. From spare and parts (speakers, wiring, transistors) to complete home theater systems, audio mixers and lighting for dance clubs. The other half of the street (from Isabel la Catolica to specializes in Stationery and Paper.
Eje Central Avenue You will notice that this street is full of street vendors. Be careful, the area is extremely crowded making it a paradise for pickpockets. Between the streets of República del Salvador and República de Uruguay, there is a shopping center known as Plaza de Computación if you have the time and are of the geeky persuation, it's an enormous indoor market of little stalls hawking computer parts and electronics, the closest thing to Chiba City you'll ever see, minus the black market cybernetics (pirate computer software and games, both inside the market, and on the sidewalks outside).
Articulo 123 street Specializes in appliances, from spare and parts to industrial vacuums and blenders.
Victoria streetSpecializes in lighting, from wiring and electric outlets to chandeliers and lamps.
Donceles street Specializes in photography.
Republica de Cuba Specializes in printing (books, posters, thesis) In this street there are a few libraries selling very old books (18th and 19th centuries)
El Palacio de Hierro 5 de Febrero and Venustiano Carranza streets. This department store was established in 1891. The name of this store, (The Iron Palace) was named like that after it was the first iron and steel building in the city. 
Liverpool (originally named as El Puerto de Liverpoool) This department store is housed in an art-deco building that was built in the late 1920's
Sanborns (Casa de los Azulejos) Francisco I Madero 4. Department store and restaurant. A must-see place for any visitor to Mexico City. Revolutionist Emiliano Zapata had breakfast here during his entrance to Mexico City in September 1916. This was the first store of the Mexican chain which was sold to Walgreens in 1946 and to Grupo Carso in 1985. There are more than 100 Sanborns stores in the country today.
Sanborns (Casa Boker) 16 de Septiembre and Isabel la Catolica streets. This department store is housed in a building completed in 1900 named "Casa Boker" after a warehouse store with that name that still occupies part of the building.
El Nuevo Mundo 5 de Febrero street. When you buy in this department store you notice it still has several old-style shopping processes. When decide to buying something, the salesman will prepare a small receipt, then you take it to the Cashier to pay.
C&A 5 de Febrero and Venuestiano Carranza streets.
Arts & Crafts
Mercado de Artesanias de San Juan Letran
Centro de Artesanias La Ciudadela
La Ideal Republica de Uruguay 36. Established in 1927. This is a good place for traditional bread, pastries and desserts. Ask for "Danes de Chocolate" the place's delicacy.
La Lagunilla and Tepito
Not far from Centro Historico, around 5 kilometers, lie two huge street markets: La Lagunilla and Tepito.
La Lagunilla Prolongacion Paseo de la Reforma and Francisco Bocanegra, just passed Eje 1 Norte. Sundays 10:00 to 16:00. This street market features antiques and other new goods such as clothing, crafts, food, jewelry and toys. It is considered safe to stroll in this street market, but try to remain in the 2 or 3 streets near Paseo de la Reforma, and those streets are Francisco Bocanegra and Comonfort, because beyond that the market eventually blends into Tepito where is a lot less safe.
Tepito Eje 1 Norte. Working hours Monday thru Sunday 9:00 to 16:00. Established even before the Spanish arrived to Mexico, this is a poor worker's neighborhood with a huge street market considered one of the largest in the world. It's a bad idea going there, this is Mexico City's black market where you can buy anything on your mind from counterfeit sneakers, pirate DVD movies and smuggled electronics to narcotics and weapons. On the literate side of things there's a huge second-hand book market with no less than 150 stalls, some with second-hand soft cover novels in english. The safest way to reach Tepito is by Metro. Line B (dark green) Tepito or Lagunilla Stations will take you straight to the heart of Tepito, but again: it's not a safe place to consider visiting, is too dangerous.
WARNING: Be careful, Tepito is a very dangerous place. If in curiosity to go try to dress with the lowest profile possible, go accompanied and be at early hours when is less crowded. If you don't speak spanish is better for you to stay away. The area is known to be home of druglords and black market dealers.
Cafe La Opera
Cafe de Tacuba, Tacuba 28. Housed in a former convent, this institution serves up tasty Mexican dishes all day for reasonable prices. No reservations accepted, but very popular so arrive early. Menu in English and Spanish.
Cafe La Opera, Cinco de Mayo 10. This restaurant has been serving Mexican food since the early 1900's and retains the same furniture since then. When you get there, look up to the ceiling, there you will see the famous gun shot accidentally fired by Pancho Villa.
Cafe el Popular, Cinco de Mayo 52. A quintessential breakfast joint offering a range of tasty egg dishes for well under USD $4 and surealistically low chrome ceilings.
Dulceria de Celaya, Cinco de Mayo 39. This confectionery shop sells old fashioned sweets. It was established in 1874 and still has its original cabinets from that age.
Ostioneria Las Palmas, in Centro. Fantastic ceviche, superior huachinango al ajillo; everything very, very fresh, very, very tasty, quickly served, and very inexpensive. Interesting old specialist shops on neighborhood streets.
La Terraza, Restaurant on the roof of the Hotel Majestic overlooking the Zocalo.
Tenampa, Plaza Garibaldi, Eje Central (In the corner of the Garibaldi square), M-Su 12PM-3AM. The original and most famous Mexican cantina, traditional home to the bohemians and mariachis of the 40s and 50s. Huge selection of tequila and mezcal, light mexican food, and mariachi bands, photographers, and "how much AC electrical current can we send through your body before you cry uncle" machines for rent. MXP100-500 (very up to you).
Hotel Principal, 29 Bolivar. Clean, friendly, and well run hotel with a range of rooms. Most overlook a quiet inner courtyard. Doubles from the low USD $20s.
Hotel Majestic, on the Zocalo. The location is great, the rooms are clean and comfortable but the service is vaudevillian. The restaurant on the top floor has a superb view of the Cathedral and Presidential Palace but the food isn't worthy of the ambience. $120 (double).
Hostel Moneda, on Moneda just off the square. Cheap but lively hostel, has a good bar on the top floor and free decent breakfast and internet. 
Hotel Virreyes Jose Ma. Izazaga 8. Cheap accomodation for backpackers. $100 pesos for a bed, $250 for a private room.
Overall, walking in the Centro Historico is safe. The best recommendation is to avoid those streets with an excessive amount of street vendors particularly in the streets behind Palacio Nacional/Zocalo because is extremely crowded. Use your common sense.