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!

How much time is it from Phoenix to Tuscon?

I've only been as far as Phoenix, so I definitely plan on exploring more of the southwest too!

Haven't been to New Mexico Yet, and Moab UT is one of the most gorgeous places, but I need to see more like Monument Valley, and so much more!
I'm studying Anthropology, so I am excited to be getting to knonw more of the Native Communities also.

Flagstaff is also worth visiting, that's about 2 hours north. There is plenty of Native American stuff to explore, there are several tribes along the outskirts of Phoenix and of course the Navajo/Hopi land in the Northeast of the state. And thanks to Barry Goldwater and Dennis DeConcini, there are a ton of National Monuments and Parks to check out - a lot of them being ancient Native ruins.

I also went through the Sunset Crater park and it was gorgeous...

so, yeah, there's enough to look at to keep me busy for a long time!! I'gotta get in shape for hiking!

But the traffic is hectic, they don't have extra roads like the eastern part of our country have so that one highway can clog up some times. Just get settled in and get a feel for the traffic timings as it is all about avoiding crush-hour there. Try and stay somewhat close to ASU, depending on your budget as the heat makes using public transport tough at times for over half the year. The other half the weather is amazing.

All the cities you mention are good. Tempe has the most social activity. I would not recommend downtown Phoenix. Ahwatukee is nice. I would suggest looking for apartments near a valley metro station. This would get you to ASU and downtown Tempe without the need to drive (thus eliminating the risk of a DUI conviction on a night out). You really need a car to get around the East Valley because of the heat and the cities are spread out. However, it is a great place to live for 9 months of the year and tolerable for the other 3. Enjoy it, I did.

but Arizona is pretty much vehicle-required. if you are coming from snow country you may have a rough time from April to November. it was still hitting 100 this month in the Phx area. it can be brutal to the point of deadly. winter in the valley is FABULOUS.

The drive across the Phx metro area can take longer than the drive to Tucson LOL it always jams around Queen Creek for no apparent reason. I 17 north of Phx to Flag and environs often gets jammed due to wrecks. Lots to explore in the state depending on interests. Plenty of readily available tourist type info since it is a huge industry here. can't speak to housing anymore, although there is a lot of new apt type stuff around Tempe now, but it has been a huge stucco and stick single home area for generations.

Once it gets too hot I can run away back to the Sierras

I have a Kia Soul, good commuter car. And I also dont mind driving on the back streets instead of freeways...I'm definitely not a stressful driver anymore LOL I grew up in the Bay Area and that commute was pretty narly.