The downtown/city center area is nice to walk around in, especially if you're not used to Spanish colonial architechture. At the main square or 'zocalo' you can see the National Palace, with the very very worthwile murals of Diego Rivera (as in Frida Kahlo's husband). Also, the cathedral is nice, as are the remains of the grand Aztec temples and the associated museum. The National Anthropology museum in the Chapultepec district is also worthwile; it will give you a great overview into the people of Mexico, and it contains the famous Aztec calendar. In the south of the city, San Angel and Coyoacan are lively artsy districts, and in Coyoacan you can see Kahlo's and Rivera's houses, as well as the museum dedicated to Trotzki. If you want to do something very very Mexican, but very touristy also, is to go to Xochimilco on a Sunday, and rent one of the "boats"/rafts (there are tons and tons for hire w/ 'driver' and all), and have a nice float around the 'gardens'.