Getting the bus or metro and seeing the daily buzz of the city.
The great Aztec pyramids, they really are impressive.
The Frida Kahlo and Trotsky museums, they are close by each other, VERY interesting and relatively uncrowded (on a Tuesday).
Wandering around the streets, particularly around Cohucacan, and sitting in the city parks.
Quick Tips:
Use the metro, it is 2 pesos(!!) per journey and quick and easy to use. Be careful which area of the city you stay in; Cohucacan is the nicest area I found (near the Frida Museo).
Best Way To Get Around:
Definitely buses (about 3 pesos) and the metro however taxis aren't exactly expensive.
There are notices of warnings about the Green VW taxis. I had no trouble with them but didn't travel in them after dark. My advice is look for the driver's Taxi license and Photo inside the car.