Best food city in Mexico
Each region of Mexico specializes in its own style cuisine. "Most diversified" will get you mediocre, in most instances, because, for example, you generally won't find great Oaxacan cuisine in Puebla, and you won't find great Puebla cuisine in Michoacán, and you won't find great Michoacán cooking in Sonora.
I believe that your best bet is to go to the source: go to Pátzcuaro, Morelia, and Ziracuaretiro in Michoacán for truly outstanding regional cuisine, go to Oaxaca for great Oaxacan cuisine--but be careful, alta cocina is taking the place by storm and has no relationship to Oaxaca cuisine--or go to Puebla for old-style Puebla cooking.
In Mexico City, there are some really fine examples of great Mexican food: Restaurante Flor de Lis, Restaurante El Bajío (the original location), Azul/Condesa, and some others. Street food is abundant, excellent, and fun to sample. Have a great trip and post back!
Mexico City could consume 4 or 5 days alone ;-)
Third for Oaxaca and second for Puebla as well.
In addition, you might want to consider:
Patzcuaro in Michoacan for the street food. It's a small manageable town with street food that's tasty and pretty safe. Corundas, nieves, atole de grano, carnitas, enchiladas placeras, sopa tarasteca, the list goes on for miles.
If you're in to seafood, Veracurz offers some options
And, don't laugh, the Mexican city doing some of the most interesting, cutting edge food right now is Tijuana. And it's only about 50 miles from the Valle de Guadalupe which one of Mexico's wine growing regions. Easily accessible from D.F. by multiple airlines.