This relatively large area in the southwest of Mexico City has always been a counterculture hotbed. This is where Frida Kahlo and Diego Rivera lived, a few blocks away from Leon Trotsky (their houses are now the Frida Kahlo Museum and the Leon Trotsky Museum, respectively), and the tranquil residential area, with parks, squares, and cobblestone streets, is now a favourite spot for the bohemia set.
Metro stations are not conveniently located to the Coyoacán center-- don't let the existence of a Coyoacán station (Line 3) fool you. Be prepared for at least a twenty minute walk from any of the nearest stations: Coyoacán, Viveros, and Miguel Ángel de Quevedo (all on Line 3). You may also approach from General Anaya station (Line 2); take the Calle 20 de Agosto exit for a picturesque twenty minute walk to the Frida Kahlo and Leon Trotsky museums. You can get a map of the subway lines, and a map of the area with the main attractions. 
If you don't fancy a 20 minute walk from Metro Coyoacan to the main square Plaza Hidalgo, you can take a microbus also known as a Pesero. These are the small green and grey busses that can be seen breaking road rules all over the city. As you leave either exit of Metro Coyoacan, cross the to the other side of the large road directly outside the metro (Av Universidad). Peseros will stop outside all metro stations, and all display their destinations in the front windscreen. Look for a sign saying Plaza Hidalgo, or ask the driver.
A cat takes the sun on top of a model pyramid in Frida Kahlo's Casa Azul
Museo Frida Kahlo, Londres 247, Col. Del Carmen, ☎ +52 55 5554 5999, +52 55 5658 5778, . Tu-Su 10AM-5:30PM. Also known as La Casa Azul, this walled hacienda painted brilliant indigo blue, is where the much-revered Mexican artist spent the last years of her life. Admission includes access to the courtyard, a small series of galleries with ever-changing displays, and the historical portion of the house, which has been preserved from the days when Kahlo was alive. A small snack bar and museum shop are also on the premises, and lectures are given periodically. An iPod tour can be taken for an extra fee.$45; $20 for student ticket; one ticket good at both here and Museo Diego Rivera-Anahuacalli.
Museo Diego Rivera-Anahuacalli, Museo 150, Col. San Pablo Tepetlapa, ☎ +52 55 5617 4310, +52 55 5617 3797, . Tu-Su 10:30AM-5PM (last tour on Friday at 4:15PM). Artist and muralist Diego Rivera built this structure to serve both as his studio and a museum to hold his collection of pre-Columbian art. The imposing neo-Aztec building sits in a parklike environment that is one of the few wildlife refuges in Mexico City. Guided tours of the main structure (in Spanish only) are given every hour or so. There is also a small gallery where art, music, and dance lessons, lectures, and concerts are held; check the placard at the entrance for details on what is being offered for the month. Secondary school groups make frequent outings.$45; $20 for student ticket; one ticket good at both here and Museo Frida Kahlo.
Museo Leon Trotsky, Viena 45, Col. Del Carmen, ☎ +52 55 5554 0687. Tu-Su 10AM-5PM. Marxist theorist Leon Trotsky was granted asylum in Mexico after being expelled from the Soviet Union, where he settled in Coyoacán in 1936. He continued to be vocally critical of Stalin's policies, however, and four years later he was assassinated in his home. The museum preserves the house in much the condition as it was in Trotsky's last days.$10.
Museo Nacional de las Culturas Populares, Av. Hidalgo No. 289, Col. Del Carmen, ☎ 41 55 09 20, . Tu-Su 10AM-6PM. This museum offers homage to the many different indigenous cultures of Mexico, celebrating folk art, music, gastronomy, and more. They also have an impressive bookshop with art for sale from skilled artisans from all over the country.
The small neighborhood around the Anahuacalli has several nice cafes and a quiet charm; it is popular with university students and creative bohemian types.
In the rough center of Coyoacán there is a pair of large squares, Plaza Hidalgo and Jardín Centenario, which are the center for a lot of the activity in the area. On Saturdays and Sundays, there's an open-air market in the squares, mostly focusing on arts and crafts, clothes (a lot of tie-dye and t-shirts), piercings and tattoos. With a bit of selectivity, and some haggling, you can pick up a lot of interesting things here, and none of them are horribly touristy or tacky. There are also impromptu African dance performances, Aztec dancers, fortune tellers, and lots more to see. The market square is surrounded by cafes and restaurants, as well as a small 16th century church and a small public library. In the smaller streets nearby are even more cafes and restaurants, as well as stores selling antiques, clothes, crafts, and so on.
Wander the old churches around the neighborhood
Inspect the interesting crafts, souvenirs, and trinkets for sale in the central squares and surrounding markets, and watch children play with various entertaining toys, balloons, balls, etc.
Buy an ice cream and/or a churro relleno (a stick of fried dough rolled in cinnamon and sugar and filled with your choice of sweet, gooey, substance).
Watch a music or dance performance
Go to at least one art/political/cultural museum.
Bazar Casa del Coleccionista, Francisco Sosa 1, corner with Tres Cruces Street. Opens Mon-Sun. This place sells lots of vintage itens, from china ware, toys, paintings, ornaments and more.
Ruta de la Seda, Aurora (cross street Pino, across from Parque Santa Catarina). Look for a small, orange stucco building, without even a sign over the door, with the only indication that it's a cafe in this residential neighborhood are the tables and chairs out on the sidewalk. True to its hippie, progressive environment, this tiny cafe serves organic pastries and coffee, and has some Indian food on the menu (samosas, mango lassi). Try the green tea cake with ice cream, also made of green tea.$20-$50.
El Jarocho, (corner of Caballocalco/Allende and Cuauhtémoc). Daily. This is a very old, family-owned coffee roaster's shop. They have really good and cheap coffee, bad and cheap tortas (sandwiches in French bread), and reasonably standard American-style donuts. There are benches on the sidewalk just outside the Jarocho shops where you can sit to drink your coffee, or you can do like everyone else in Coyoacán and just stroll around the park with your Jarocho foam cup in your hand. On weekends, expect to wait in line to order your coffee. A long wait in line for coffee, a bag of fresh churros, and a conversation in Cuyoacán's plaza is an quintessential Mexico City date.$10-20.
Bizarro, Cuauhtémoc (between Centenario and Aguayo). Daily. A comfortable goth hangout. There is a really good bakery next door.$30-100.
Café de la Selva, Plaza Hidalgo (next to the church atrium, at the back of the archway). Open daily. A perennial student hangout, also serving baguettes and cakes.$50-100.
Oyster and shrimp ceviche from El Jardin del Pulpo
El Morral, Caballocalco (20 meters North of Plaza Hidalgo). Daily. Very good Mexican food. Don't miss the chiles en nogada, large chiles stuffed with ground beef, raisins, and nuts, and covered with a nut cream sauce. Their hand-made tortillas are fantastic. Service can be a bit slow though.$100-300.
El Jardin del Pulpo, Mercado Coyoacan, Malintzin 89 L24-25. Daily until 6PM. The "Octopus's Garden" is a casual marisqueria, or seafood place, featuring ceviche, seafood paella, whole roast fish, and even fish and chips. It's located catty-corner from La Casa Azul. Dining is cafeteria-style at long tables under an awning. If you want fresh juices, agua frescas, or ice cream, those are available from two shops next door.$50-300.
Los Danzantes, Centro de Coyoacán (on the corner of the main market square in Coyoacán). Daily. Somewhat pricey modern international cuisine with twists on traditional Mexican dishes. They also bottle and sell their own brand of mezcál. Try the seafood-chilpotle chili soup, the goatcheese-filled chicken breast with chilpotle chili sauce, and, if you can afford the $200 price tag, the escamoles (ant eggs) sol azteca as a starter (small, but can be shared between two people).$250-500.
La Guadalupana, Higuera 14 (60 meters west of Plaza Hidalgo). M-Sa, closed Su. Very good Mexican food. Good drinking with the locals. Don't miss the "Mole," "Michele's favorite" or carne tartara. Their hand-made tortillas are fantastic. Service is good, make friends with the Meseros; they are cool.$100-300.
Taro, Av. Universidad (a block and a half from Miguel Ángel de Quevedo, going towards the UNAM campus, across the street from the Novo bookstore and the Pasteur pharmacy). Th-Tu. Probably the best Japanese food in Mexico City, owned by Japanese. Many Japanese people come here for lunch and dinner, so they attest to the authenticity of the meals --- you won't find maki rolls with cream cheese here. Don't miss their spicy octopus entrée and the ice-cream tempura for dessert.$150-300.
Las Nieves de Coyoacán, Carrillo Puerto (across the street from Plaza Hidalgo, 30 meters from Jardín Centenario). Daily. One of the best sorbets in the city. Try the ones made from exotic fruits: guanábana, zapote, maracuya, tuna (cactus fruit). The coconut-flavored paletas (popsicles) are also a treat.$20-50.
Nieves el Tepozteco. A few steps away from Las nieves de Coyoacán, features excellent flavors such as Beso de Angel (angel kiss), Mil Floes (thousand flowers) and spicy sorbets!
Churreria de Coyoacán, Ignacio Allende (near cross-street Cuauhtémoc). Churros are not too popular in Mexico City, but there are a number of places in Coyoacán (including street stands) that have them. The Churreria is a good place with excellent churros and you can fill it with a number of ingredients, like chocolate, fresa (strawberry), durazno (peach), lechera (milk), zarzamora (blackberry) and more.$7-$10.
Street food. The main plaza, at different times of the year, might have street food vendors that sell extremely good flautas (long, deep fried tacos), as well as buñuelos (deep fried sugar-coated bread), esquites, and elotes (corn with chile, mayonase, lime, and cheese).
El Chupacabras, Close to Metro Coyoacan (Under the highway at the intersection of churubusco and universidad). Open 24 hours. These are some of the most famous street tacos in Mexico City. Their speciality is the chupacabra taco, a combination of pork, beef and a 'secret ingredient'.
El Hijo del Cuervo, Jardin Centenario 17, Coyoacan, ☎ 55/5658-5196. Locals pack El Hijo del Cuervo which plays a mixture of rock and protest music. Cover charge is usally $7.
El Vicio, Madrid 13, Coyoacan, ☎ 55/5659-1139. Cabaret venue that showcases music, theatre and cabaret shows. Shows are in Spanish.
There are not many hotels and hostels in Coyoacan, but do try the following:
Coyote Flaco Backpackers, Av. México 112, Col. Del Carmen. Hostel that has 40 rooms all with private bathrooms. Great place to meet fellow travelers, and the staff and helpful and friendly.
Suites Coyoacan, Avenue Coyoacan 1909 Colonia del Valle Mexico City 0310. Standard hotel that offers comfortable sized rooms at an affordable price. The location is the big drawcard though, less than a block from the Coyoacan subway station, which is about a half hour from downtown. It is also within walking distance (30 min) to two parks that have really great restaurants all around.$100.