Mexico City Regions - Centro
The old city center of Mexico City, around the Zócalo, is a very large area with an enormous amount of stores, street vendors, and people. Most people here walk, as it's the easiest way to get around in the sometimes narrow streets. Apart from the Zócalo itself and the surrounding historical buildings and museums, things worth seeing include the art deco opera building "Bellas Artes" by Eje Central (the whole area surrounding the opera is full of wonderful art deco buildings). Close to the opera is the Latinoamericana tower, an old-style highrise building with a viewing gallery and small cafe in the top floors (entrance is 35 pesos per person), from which you can get a very good view of the entire downtown area. Going up here is much more worth it if it's a windy day, the wind clears the smog away and makes the view truly spectacular.

A couple of blocks south along Eje Central are the streets of República del Salvador and República de Uruguay, which are full of computing and electronics stores. Enter the Plaza de Computación if you have the time and are of the geeky persuation, it's an enormous indoor market of little stalls hawking computer parts and electronics, the closest thing to Chiba City you'll ever see, minus the black market cybernetics (but pirated computer games are readily available, both insides the market, and on the sidewalks outside)