The food is a big part of the culture of a country, in Mexico the food has been subjected to a lot of influences since the arrival of the Spanish and their conquest.
America gave the Old Continent a lot of new ingredients and recipes, but also got back some in return. Prehispanic/Precolumbian real food is still around but is not the norm in big cities. Although some of the dishes are real delicacies that can cost a lot of money depending on the type of restaurant or availability (some ingredients are very scarce especially seasonal ones).
Quick Tips:
In Mexico, the real food is not the one found at high priced restaurants in the touristic zones. Some of them will provide a Mexican menu, but there is no warranty that the plates would be truly Mexican instead of a Mexicanized version of the same idea blended with "nouvell cuisine". If you want to taste the real thing you have to eat where the locals do (like any other place in the world that you visit), and by locals I don´t necessarily mean the masons building houses nor the blue collar Elite, go where average people would eat, even in touristic areas.
If you are in Mexico City you can have safe food near the touristic areas but not necessarily the tourist traps. At lunch time follow the office workers, they will head to a "fonda" normally a Mom & Pop place that serves a menu called "Comida Corrida" consisting on a Soup, an entree, a main dish, and dessert. Soft drinks may or not may be included in the price which tends to be very affordable around 40-60 pesos (June 2006). Depending on the particular "fonda" the soft drink can be a mass produced fresh fruit drink and in some of this places you may drink up to a jar of it included in the price, that makes for a really cheap meal.
Best Way To Get Around:
In Mexico City there are good places near the tourist zones.
Polanco. Ask your concierge for the "food area" between Polanco and Parque Lincon, there you can find good quality, clean restaurants, and a wide variety of real Mexican food, from tacos to tortas to roasted chicken and comida corrida.
Condesa. This area is famous for its restaurants, some of them are on the high end of the price range and tend to be more Fusion than Mexican, but stroll around and you will find something for your budget.
Paseo de la Reforma and Avenida Juarez corridor. Like in any tourist area of the world and especially ports, walk one block further than the main avenue and you will find real bargains, try to find where the office people eat and you won´t be disappointed.
Zocalo and Centro Historico. All around the area you will find an unimaginable variety of restaurants, some even have pre-columbian menus and offer things you would have to think twice before ordering (does fly larvae sounds appealing to you? or toasted crickets? corn fungus?) If you are not sure, try asking someone who already ordered and ask if you can have a little taste of their food, most of the people are friendly and understanding enough that they will be glad to share with you.
Coyoacan. Around the main square of this Colonial in town you will be able to find excellent restaurants with true Mexican flavor and menus. There is a famous Cantina called La Guadalupana, is more expensive but it depends on your tastes. If you want a more common place to eat there is the Food Market a few steps in the back of the cantina, offering all kinds of local dishes. A couple blocks north you find the local market which have a bit of everything including fruit and food stands.