Coyoacan is a nice leafy well-to-do neighbourhood, famous for the Frida Kahlo museum. It has lots of nicely painted houses, which reminded me a bit of Barranco in Lima, but without the colonial mansions. There is also a nice square there, with a few funky bars and restaurants. The market is also worth checking out. I wouldn’t recommend staying here, as there are few budget options and it is quite a distance from the historical centre, where most of the tourist attractions are. And taking the L3 subway line during rush hour is an absolute nightmare.
The University of Mexico is absolutely massive. You take the L3 Metro to get there, but then to traverse the grounds, you have to jump on one of the free buses. These are rammed with students trying to get from one faculty to the other. The highlight is the library, which features a huge mural designed in the 1950s. Just near the library is the 1968 Olympic stadium, but unfortunately it is closed to the public.