I have always loved Mexico City. The places you need to see is the Palace on the hilltop in Chipultapec Park, the National Zoo with the Pandas. Go to Guadalupe Cathedral. Go to the pyramids outside of Mexico City. The Archeological (excuse the spelling) Museum. Be sure to take more than one day to see the Museum. I would advise you ride the subway system as much as possible. Stay out of the back streets. Your best bet is to stay in the "Pink Zone" area. The city is constantly covered in smog unless you are very lucky, because the city sits in the floor of a volcano. I forgot don't forget to see the National Cathedral and National Zocola. The whole city is fantastic, that is if you can breathe.
I have been there at least 20 times, and only once have I been there when the smog was clear, and you can see the surrounding mountains, which are snow capped. The country is like going into another world. The food is fantastic. Can you tell I like Mexico City?