How many days will you be there? Cinco de Mayo is really only celebrated in Puebla. The rest of Mexico recognizes the date, but don't expect anything out of the ordinary to happen.
We (my wife is from Mexico, about 1 hour north of Mexico City) wrote up a suggestion list for a friend's daughter that went recently. This is very convenient, since I can just copy/paste here----
Be sure to go somewhere for comida corrida. Its a cheap lunch place that makes just a set amount of food each day and you only get a couple of choices. Usually about $4 from 12-2:00 with soup + entree with rice or beans + tiny dessert + pitcher of water/lemonade/orangeade/tamarindo. Very simple with plastic chairs and will probably share a table with other people. If you arrive late, they'll probably be out of food.
Historic center--- Zocalo, Palacio de Bellas Artes, restaurant Casa de los Azulejos for lunch, Cathedral, Torre Latinoamericana (pay to go to top for view), Templo Mayor (ruins), various museums, check schedule for Palacio de Bellas Artes because they often have very good shows for cheap
Castillo de Chapultepec + Zoo-- palace from the French occupation, zoo nearby
Anthropology Museum
Teotihuacan an hour from the city, there's bus from Central Norte, very big Aztec site
Coyoacan is a neighborhood in the center of the city--- Colonial style, well preserved, expensive, hipsters live there, music at night, very alive, has all the vibes of a small country town center, there is a museum for Frida Kahlo
Day trip to Toluca-- train from El Insurgente or bus
Xochimilco--- tourists love it, play music as they take you on boats, colorful, Mrs.Uniwelder doesn't like it because it smells of methane swamp
La Zona Rosa and Polanco-- rich neighborhoods with fancy restaurants and shops and nightlife, if she's into that (we're not)
Bellini--- restaurant with rotating top for panoramic view while dining, need reservation, good for a date and one time experience