Maybe it's hard to recommend you places to visit in Southern Mexico City because... There are so, so, so many! 🙂
We live very close to our National University campus (UNAM, Ciudad Universitaria). The campus is in the UNESCO list of cultural heritage, and very well worth a visit. Try to visit in weekdays, so you can also go to Espacio Escultórico, ~2Km South of the central campus. I think it opens from 9:00 to 16:00. Or, in similar hours but also on weekends, to the beautiful Botanical Garden.
Coyoacán is a beautiful neighborhood with many cafes, opportunities to buy all kinds of handicrafts, many interesting museums (Leon Trotsky's house, Popular Cultures museum, the famous and in my opinion overrateed Frida Kahlo's Blue House, and others).
San Ángel has somewhat of the same spirit of Coyoacán, although... different. And if you are looking for fine, unique handicrafts to buy (of course, for more money), that's an even better option.
The small Cuicuilco archaeological site is small, very interesting; it is one of the oldest pyramids in Mesoamerica, from before the Xitle's eruption that changed the whole South West of our city (>2000 years ago). It is also the only conic pyramid I've seen in Central Mexico.
I've only mentioned places that are in walking distance (<5Km) from my home. There is much, much more to enjoy in this corner of the city!