Museo Frida Kahlo
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.
Museo Diego Rivera-Anahuacalli
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.
Museo Leon Trotsky
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.
Museo Nacional de las Culturas Populares
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 JardÃn 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.