Someone told me that Mexico City has 150 museums. It is impossible to see everything. I will mention a few attractions on this page, will add more between now and the meeting, and welcome other suggestions.
Stone engraving of "the ballgame"--a popular exhibit at the Anthropology Museum
Museo Nacional de Antropologia–situated on the edge of the beautiful Bosque de Chapultepec (see below), the National Anthropology Museum is a vast and comprehensive complex showcasing ancient regional cultures from around the country including the Aztecs, Zapotec, Mixtec, Olmec, Tontonac, Huastec, Maya and other civilizations
Museo de Arte Popular–this private art museum features fine specimens of typical Mexican crafts. If you like folk art it is not to be missed. Also a great gift shop.
Outside the Museo Popular
Palacio de Bellas Artes–this is concert venue at the east end of the Alameda Central Park. It has a famed Tiffany glass curtain that you can only see if you attend a concert. But the hall is open to visitors, and
the second story is ringed with fabulous murals by Rivera, Orozco and others, including the famous mural Diego Rivera painted on commission for Rockefeller Center in New York which was too political for his patrons in NY.
Zocolo–this enormous square is the heart of the city and the center of the Centro Historico. It is home to several key sites that are essential parts of a visit to Mexico City.
Templo Mayor–astonishingly, an Aztec ruin sits right in the middle of the Zocolo. In 1978, electrical workers stumbled upon an 8 ton carving of the Aztec goddess Coyolxauhqui. Subsequently, the entire site was excavated. It is said that this spot was considered to be the center of the universe by the Aztecs.
Palacio Nationale–this building stands on the East side of the Zocolo, the city’s central square. It is still in use as a federal government building. Notably, it houses 1,200 feet of murals by Diego Rivera depicting the history of the nation.
Catedral Metrepolitana–construction on this cathedral, which stands on the north side of the Zocolo, began in 1573 and continued for 3 centuries.
The Coyoacan District–a suburb on the southern end of city where Frida Kahlo and Diego Rivera lived. The neighborhood is home to several small museums containing their work.
Xochimilco–a town 14 miles south of the city known as the “place of flowers”. 
Flower laden canal boats glide through town.
Teotihuacan–(see photo at top of the page) the ruins of what was once the largest city in pre-Columbian America, possibly one of the largest cities in the world in its time. Features include murals, the pyramids of the sun and moon, and the avenue of the dead. The city was built between the first century AD and 600 AD. The Pyramide del Sol is the world’s third largest pyramid. Teotihuacan is just one hour from the city.
Bosque de Chapultepec–the city’s largest park, home to two museums, a lake for row-boating, and two museums. Sunday is purportedly the most vibrant day, with families picnicking and dozens of vendors along the paths.
The Voladores (flying men) outside the Anthropology Museum
In front of the entrance to the Anthropology Museum, on the north side of the park, indiginous Totonoc from Papantra men perform their incredible voladores (“flying men”) rite several times a week.
IPA Mexico City 
I am so glad for your appreciative look at Mexico City. Mexico City is an oasis for human rights. It is governed by a leftist party, inspired by cardenismo. Cardenas expropriated in 1938 the U.S. and English petroleum companies.
I would suggest that those interested in paintinga, surrealism and gender, explore in the Museum of Modern Art, on Paseo de la Reforma , the works of 3 surrealist 20th century women painters in Mexico:Frida Kahlo, daughter of a mestizo Mexican woman and a Jewish German father photographer , Eleanora Carrington, English, wife of Max Ernst and who escaped from a Portuguese mental hospital and Remedios Varo, refugee from Franco´s fascist Spain.