I'm on the West side, and don't know much of the Chandler/Mesa/Gilbert area. I can say that downtown Phoenix and Tempe are both blue, while Chandler/Mesa/Gilbert are red. The further out you get the rent gets cheaper, but you'll have a longer commute - and the areas around the downtown and Tempe campuses are probably the worst parts of town for finding parking. Still not that bad - the city is very car friendly.
As far as food, we have great Mexican food, and a little bit of Native cuisine - not as much as you'd expect. The one place I know is Fry Bread House, and they are excellent.
Definitely try Barrio Cafe (if it's still around, they was talk about it closing earlier this year). The chef/owner is a queer lady who is a big supporter of Democrats and has hosted events/photo ops for our candidates. Los Dos Molinos is another great one, there are locations in downtown and in Mesa that are great if you like spicy New Mexican style food.
Also try Pizzeria Bianco. It has consistently been judged the best pizza in America, and its owner Chris Bianco is a bit of a celebrity chef. The problem is it only seats about a dozen people, so the waits are long. There is an attached bar you can usually get seated easily at, and still order from the same menu. Bianco has another Italian restaurant, a coffee house and bakery as well.
Another local gem is Cornish Pasty Co, they are based here and have multiple locations around town. You'll also want to try a Sonoran Dog, a southwest style hot dog from Mexico that is wrapped in bacon and topped with beans and chiles - Tucson is really the place to get those though. Tucson has a host of great Mexican restaurants as well, especially El Charro Cafe.
As far as other cuisines, the Valley is developing a good food scene, but its nowhere near the level of other big cities yet.
Hope this helps!