Mexico City is a city you walk and eat rather than one you book, but a few things are worth arranging.
Food tours are the best value. The street food here is the best argument for the city and the thing visitors are most nervous about; a guide who knows which stall has been in the same doorway for thirty years solves that in an afternoon. The good operators walk and use the metro.
Lucha libre at the Arena México on a Tuesday or Friday is genuinely a spectacle, and the tours exist mostly to handle the tickets and get you there and back — you can also simply buy a ticket at the box office.
Xochimilco, in the far south, is what is left of the lake the city was built on: canals, flat-bottomed trajineras poled between chinampas, mariachis for hire, and — behind it — a working agricultural system a thousand years old and the last wild habitat of the axolotl. Go on a weekday if you want the canals rather than the party.
Out of town: Teotihuacán, an hour northeast, with balloons at sunrise; Taxco, the silver town; Puebla and Cholula; Valle de Bravo; and, from late October to March, the long day east to the monarch butterfly sanctuaries.