Pia: you are going to love Mexico. I suggest that in addition to the place you will live at in Mexico, you also consider visiting the following places (however, remember that Mexico is probably 2 1/2 times the size of a country like Spain):
North: Go by train from Chihuahua City to the town of Creel to visit the Copper Canyon
Gulf of Mexico: Visit the City of Veracruz and the town of Catemaco
Central Mexico: The Pyramids of the Sun and the Moon in the State of Mexico; Mexico City also has some really nice areas like Polanco, Chapultepec, Ave. Insurgentes, the old Basilica, etc; the City of Puebla (just 1 ½ from Mexico City, look for crafts and traditional candy there).
Central-North: the cities of Guanajuato (very bohemian and artistic), San Miguel de Allende and Queretaro (beautiful little plazas and tons of churches).
Southern-Mexico: Oaxaca (a great example of Colonial art mixed with native art), Chiapas (beautiful scenery), and Merida (very unique food).
Occident: The City of Guadalajara in the State of Jalisco (where Mariachi music and tequila are from).
As to tourist areas: Acapulco (close to Mexico City), Los Cabos (in north-Mexico), Cancun, Isla Mujeres, Cozumel, and Huatulco in the very south. Puerto Vallarta on the
Pacific (closer large city is Guadalajara).
And there's much more, but if you get to most of those places you will get a good understanding of the different foods, traditions, folklore, and lifestyles in the different states of Mexico. If you have to choose between one area and the other, I will definitely go central and south Mexico, I personally think it is more charming.
Buena suerte!