As if Mexico city didn't have enough to do and see, you have to also strongly consider doing a few day trips if you have the time.
The pyramids of Teotihuacan have a unique story and are an important part of Mexican history. They city is believed to be the largest in the pre-Columbian Americas. The actual name of the city is unknown, but the Aztecs named it "Teotihuacan" or "birthplace of the Gods". This is because the Aztecs believed that the gods created the universe at that site.
The city is about two hours from Mexico City and extremely worth visiting. I thought it was beautiful to see these ruins. They are extremely well preserved! There must have been so many stories here of families and a community that was definitely ahead of it's time.