Posh neighbourhood in the Southern part of Mexico City, easily accessed from the Taxqueña or Miguel Angel de Quevedo tube station by pesero.
Notice that the Coyoacan metro is as inconvenient as hell.

In Coyoacan there are a couple of nice churches and beautiful squares, most notably the Plaza de la Conchita. In the main square there is a vaguely alternative market on Saturdays: there you can buy cheap paraphernalia, overpriced arts and crafts, have various parts of your body pierced.
Among other things to visit here, there are the house of Frida Kahlo and Diego Riviera, the house where Lev Trotzky lived for some years and where he was murdered and the Ex Convento de Churubusco, home to the Museum of Foreign intervention in Mexico. Needless to say, the US play a big part in it.

Coyoacan is one of the safe parts of Mexico City: you can walk around here after darkness, and usually nothing terrible will happen to you.

The best place for eating in Coyoacan is the mercado, quite close to the main square.