Here is a long list of things to do in the city - see the other posts for more information on each:
National Palace (Palacio Nacional)
Palacio de Bellas Artes - Theatre
Museo de Arte Popular - The museum of Popular art, a great musuem housing many mexican works
San Jacinto Plaza - San Jacinto Park
Ballet Folklorico de Mexico - Mexican Ballet
National Museum of Anthropology (Museo Nacional de Antropologia)
Plaza de las Tres Culturas - the plaza of the three cultures
Edificio de Correos - The post office building
Museo Leon Trotsky - the house was built just before the mexican revolution and is a great piece of history
Castillo de Chapultepec - Chapultepec Castle
Zócalo - Mexico Cities large plaza, the second largest after Red Square in Russia
Museo del Templo Mayor - Templo Mayor Museum
Monumento a los Ninos Heroes - Famous and Important momument
Central University City Campus (UNAM) - One of the countries best Universities and a great peice of Architecture
Metropolitan Cathedral (Catedral Metropolitana) - One of the cities best sites
Museo Casa Luis Barragan - The musuem and preserved home of famous mexican architect Luis Barragan
Torre Latino - go up to the top floor of the Torre Latino for great views of the city and the worlds highest aquarium located on the 38th floor
Frida Kahlo Museum (Museo Frida Kahlo) - The blue houe where the famed Mexican artist was born and died
Paseo de la Reforma - one of Mexico cities principle streets which hosts various exhibits throughout the year
Museo de Cera de la Ciudad de Mexico - Located in an old mansion, this museum chronicles the history of Mexico's capital city from the time before European contact to present day
Basilica de Santa Maria de Guadalupe - This famous Basilica, located on the site where an Indian claimed to have seen the Virgin of Guadalupe in 1531, contains an image of her that is the most famous religious icon in all of Mexico
Catedral Metropolitana - one of the largest cathedrals in Latin America
Papalote - the childrens museum with lots of things to do and see and complete with an IMAX cinema
Coyoacan - Once a small town outside the capital, it is now well within the city limits but preserves its small-town atmosphere and colonial architecture. A quiet refuge from the hustle and bustle of the city
Museo Dolores Olmedo Patino - the musuem hosts 27 works of Frida Kahlo
Xochimilco - the canals located to the south of the city which can give visitors a view of what the city looked like in pre-hispanic times
La Opera - This old bar still has the bullet holes left by Pancho Villa on one of his visits