Mexico City is one of the world's cultural Meccas. The city center is beautiful and has numerous architectural gems - Catedral Metropolitana, Palacio Bellas Artes, El Zocalo, MUNAL, etc...
Make sure that you go to Chapultepec and visit the Castle, but most importantly visit the Museo de Antropologia. This is the most important ancient art collection in Mexico and one of the best in the world. I am not sure if you are interested in archeology, but the original mask that the Mayan ruler of Pakal was wearing when they uncovered his tomb is displayed in this museum.
Also, if possible, visit Catedral de Guadalupe and Teotihuacan. Zona Rosa is where you will find anything and everything gay.
I hope you enjoy the city as much as I did. I loved it and can't wait to go back.