Mexico City: Where to stay, What to do?
For the Frida Kahlo museum, go on a day other than Sunday if possible. On Sundays, Mexican citizens enter for free. We stood in line for about 30 minutes to enter as a result. I suspect that on weekdays you might walk right in.
If you have any interest in the indigenous cultures and artifacts, do not miss the Anthropology Museum near Chapultepec park. Their collection is truly outstanding.
For our two trips to the city, we stayed in very American hotels, once at the Hyatt in Polanco because I wanted to stay on points, and once at the Hilton Reforma because we were attending an International Living conference at that venue. Both are fantastic (and priced to match!), but they don't give you a flavor of the city.
I hear a lot of people recommending the Red Tree House as a hotel.
Enjoy, and eat lots of tacos!