Coyoacan

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 hippies, goths, musicians and artists.

In the rough center of Coyoacan 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 (temporary or otherwise, but if you feel the urge to have some body art done, it's better to walk a few blocks to the south, to Dermafília, Mexico's best and most renowned body art studio, close to the corner of Carillo Puerto and Eje 10). 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, fortunetellers, and lots more to see. The market square is surrounded by cafes and restaurants, as well as a small 16th century church. In the smaller streets nearby are even more cafes and restaurants, as well as stores selling antiques, clothes, crafts, and so on.