The main square of Mexico City, Zocolo is the third largest square in the world. It is the location of the Templo Mayor and the Metropolitan Cathedral .
There are activities galore at the square and with plenty of hotel rooms around the Zocolo it makes a great (and safe) place to stay. The Zocolo is across from La Palacia Nacional, the office of the President of Mexico.
The blocks surrounding the Zocolo are chock full of both restaurants and food stands as well as shopping. It is an easy walk (or taxi ride if you're so inclined) to many of the city's cultural exhibits.