The sinking Cathedral on the main Zocalo, the ruins of Tenochtitlan - the origin of the City, Chapultepec Park, a favourite weekend spot for many city dwellers, Coyoacan, the artisan district and home to a number of museums as well as small plazas and cobbled streets.
Here you can visit the 'Blue House', once home to the artists Diego Rivera and Frida Khalo. Although still in the sprawling city, Coyoacan does present the illusion of being a small town. There is also the Torre Latinoamericano, located at the end of the Alameda, which offers bird's eye views of the city.
Be sure to let your bank know your travel itinerary so they don't put a freeze on your account when foreign transactions are made!