The Casa Rosada is Argentina's government house. Plaza de Mayo is in front of it, and there are several noteworthy buildings around the plaza, including the National Bank and Bank Museum, and the Metropolitan Cathedral.
Florida pedestrian mall is good for shopping and also for watching the street tango dancers and other performers
The Obelisco looks suspiciously like the Washington Monument. From its base is a good vantage point for Avenida 9 de Julio, which at 22 total lanes is the widest street in the Americas.
Confiteria Ideal at Suipacha 384, is a famous tango venue featured in many films. The building itself has beautiful architecture, and there are tango lessons and Milongas (dance parties) offered there daily.
Palacio Barolo at Av. de Mayo 1370. Don't miss this architectural gem in Buenos Aires, designed in accordance with the cosmology of the Divine Comedy. Reserve a guided tour in advance (night or day)  and enjoy one of the best views of Buenos Aires.
Casa de la Cultura, at Av. de Mayo 575. This is the Government Cultural House of Buenos Aires. Check out the "Salon Dorado", which design is inspired by the Palace of Versailles. Also, the Salon Dorado hosts music performers every Friday 7 PM.
Libreria La Calesita, at Av. de Mayo 769. Don't miss this antique bookstore with plenty of toys dating back to more than 50 years ago. It looks like it has been freezed over time. Jose Luis, who has been working here for more than 20 yeats, will give you advise and recommend you books according to your interests.
La Botica del Angel, at Luis Sáenz Peña 541. Church/Old House that offers guided tours and where many cultural events take place. It is considered one of the places where "cafe concert" started.
""Pasaje La Piedad"", Bartolomé Mitre 1525 y 1531. For many, one of the most beautiful "cul-de-sac" in the city. Woth going.
Walk along Avenida de Mayo: Buenos Aires is one of those cities where the best way to get immersed into it is by walking, walking and walking. With Plaza de Mayo as it starting point, Avenida de Mayo offers a beautiful walk tour. Here you will find many historical buildings, like the traditional Cafe Tortoni, or the impressive Palacio Barolo (which offers one of the best views of Buenos Aires, ask for the guided tour) .
Linea A original subte train
Take a Subte ride in Linea A: With a station at Plaza de Mayo, the Buenos Aires Subte Linea A is the oldest metro station in the city, and was the first metro line in South America. The nice thing is that many of the original trains are still in use. These were built by a the belgian company La Brugeoise, and today represents the oldest trains in commercial use in the world. They are made of wood in the inside, with manually operated doors. It is a really nice experience.
Florida pedestrian mall has a good variety of shops as well as street vendors.
Galerias Pacifico on Avenida Cordoba at Florida is an upscale shopping mall, which is worth seeing even if you don't buy anything. On the top floors is the Centro Cultural Borges which usually has art on display.
Dora. Recently moved two blocks up from it's home of over 60 years, Dora has a new, more upscale decor to match the upscale seafood. The extensive menu offers fish, meat, chicken, and one or two vegetarian options, but seafood is definitely the focus. The prices look high, but some of these dishes involve lobster and caviar. Any of the dish for two make for a huge and affordable meal. Many of the appetizers, like snow crab in avocado, would also make a filling main course for one.edit
Cafe Tortoni, at Av De Mayo 825, , one of the most traditional coffehouses in Buenos Aires. It has been restored to its original style, which dates back to 150 years ago. It was a cultural meeting point of many famous people, like Borges, Quinquela Martin, Molina Campos, among others.
Confiteria London City, at Av. de Mayo 599, , a london style bar. The original building was completely destroyed by a huge fire. It was rebuilt and opened again in 1954. Good place to stop by for a coffee before continue your walk along Av. de Mayo.
Bar Iberia, at the corner of Av. de Mayo and Salta street. After cafe Tortoni, Bar Iberia is the second oldest bar in Buenos Aires. It represents an historical significance for the city, since It used to be the meeting point for the spanish immigrants representing the 'republicans' during the civil war in Spain. In the corner in front of it, it is located Cafe Español, the meeting point for the opposite group of the republicans: those representing the Francoism. Today, Bar Iberia has been restored in a way to maintain most of its originall façade.
La Puerto Rico, at Alsina 416. One of the most popular coffees among locals, not touristic. It has been declared as "Site of Cultural Interest" by the Government of Argentina.
Apartment 'Argentina to let', Lavelle & Callao, ☎ 48241256, . 2 bedrooms (4 people max) apartment on a nice street$380 per week. edit
Casa de Papa, Avenida de Mayo 1460 (Near Plaza Congreso, right at the Subte A station Saez Pena), ☎ 54 (11) 4383 6755, . Located in the very center of Buenos Aires, Casa de Papa is a small, cozy hostel for those looking for more personal attention. The owners are very friendly and love to help make your stay the best it can be. They offer discount bus and plane tickets to their guests, have a fully equipped kitchen, hot water, wifi, and delicious breakfast. Minihostels.com members get 10% off every night they stay.7.50-12.50. edit
NH Jousten, Avda. Corrientes, 280, . Built in the early 1900’s, this hotel is perfectly situated in the heart of the city. Many well-known areas are in walking distance such as Puerto Madero, Plaza de Mayo and the famous Calle Florida street. The hotel contains a restaurant, bar and a gym, from $166.01.edit
V&S Hostel Club, Viamonte 887 (Capital Federal) (500 meters from the Colón Theater, the Obelisco, pedestrian and commercial streets Florida and Lavalle, and Corrientes Avenue), ☎ (54 11) 4322 0994 / 4327 5131, . The V&S Hostel Club is in a beautiful refurbished house whose history dates back to the 19th century. It is located in the heart of Buenos Aires and combines both the old with the new. The rates include daily maid service, luggage storage facilities, breakfast buffet style, sheets/blankets, individual bathrooms, heat and ceiling fans in all rooms.edit