The first day we were here we took the subway for a bit and went to the National University, which is absolutely gorgeous. The campus is situated in the cradle of the mountains (which are green and always seem to have clouds hovering at the top).
Later the first day we went to a "music" district near another of the city's universities. There were people everywhere, even late into the night. The area was filled with lots of little bars, restaurants and jazz clubs. Street vendors are all over the place as well. My favorite thus far has been a stand where you could buy masks, and your options were: a horse head, a camel head, Osama bin Laden, and George Bush.
On day two, at night, we walked down to a really cool district where pretty much everything was covered in neon. Malls here are quite different from what they are in the states. Here the malls are in high-rises, so each floor has two or three restaurants/shops.