I am not a big fan of archaeological sites but I visit some from time to time. Instead of writing about this site (which can be found elsewhere, starting from Wikipedia) I will just post pictures and leave some tips on how to get there from Mexico City.
Visiting Teotihuacán on your own is super simple so watch out for tours that will cost you almost three times more. To get there you will have to take a 40 Pesos (3 USD) bus from “Autobuses del Norte” bus terminal (located by the subway station with the same name, yellow line). Departures are every 15 minutes and it takes an hour to get to the ruins. Entry ticket to Teotihuacán will cost you 57 Mexican Pesos. Going back to Mexico City will cost you another 40 Mexican Pesos, you should catch a bus from the same spot you got off on your way in. And the most important thing: bring the sunscreen.