Coyoacan used to be a separate town from mexico city and now it´s one of the city´s Southern neighborhoods. public transportation in the area is not very efficient so i would take a cab (always call a station first, don´t take cabs on the street!). Coyoacan is one of the hippie and artsy parts of the city. a lot of young people go there at night and during the weekends. and there´s a lot of options in terms of food and entertainment.
don´t miss the "Casa Azul", Frida Kahlo's Blue House museum. it´s magical!!!! it´s one of my favorite places in the world! (i am a big Kahlo fan). Trostky´s former house, now museum is also in Coyoacan but I haven´t been able to go yet. friends tell me it´s very interesting as well.