I can't help you in Phoenix (and, given that Phoenix is really a surprisingly Anglo city, I'll be interested to see if others can), but when you come to Tucson (down in what once was the Gadsden Purchase, the Hispanic part of Arizona) I recommend you keep driving to a couple of places down I-19 near where I live (in the winter). Both are near Tubak, AZ, an upscale "artist colony" maybe 40 miles south of Tucson and 20 miles or so north of Mexico (come a few hours before dinner and go shopping among the seemingly hundreds of shops featuring original arts and crafts and imported Mexican handicrafts--the handmade mesquite furniture is especially stunning).
The first restaurant I'd recommend is Wisdom's Cafe' ( http://www.yelp.com/biz/wisdoms-cafe-tumacacori
), a slightly quirky little family-run place that attracts crowds and lines waiting for them to open at dinner time on weekends during the prime "snowbird" months of January - March. This place is in Tumacacori, just south of Tubak on the frontage road, near the site of a partly ruined 17th century Mission, San José de Tumacácori
. On the grounds of the mission, by the way, during the daytime you will often find locals selling good indian "fry bread". Wisdom's has fairly standard Sonoran/Mexican food done well by people who care. I learned about it first by asking a local handyman who spoke Spanish-accented English where his favorite Mexican place was and he said Wisdom's was the place his wife always made him take her.
The second is in Tubak itself and considerably more upscale (though not actually "high end"). It's called Elvira's ( http://www.yelp.com/biz/elviras-tubac
) and once it was located south of the border in Nogales, Sonora (actually just across the street from "the fence"). When it was in Mexico, it was a popular lunchtime destination for shoppers from El Norte. But all the drug violence drove away the customers and somehow they managed to move north themselves. Anyway, they built a beautiful location in Tubac and, while it seems like the prices are somewhat higher and the menu more limited, it still offers some of the highest quality Mexican food I've had in Arizona in a lovely space.
Finally, if you can't or won't take this little drive from downtown Tucson, then I would recommend Cafe Poca Cosa, especially the "little" version ( http://www.yelp.com/biz/l..e-cafe-poca-cosa-tucson
). There is also the other big sibling ( http://www.yelp.com/biz/cafe-poca-cosa-tucson
) but I like the little one, especially for lunch. They offer excellent somewhat "nouveau" Mexican fare made with the freshest and best quality ingredients available and the result has always been much tastier than the standard, rather bland Mexican fare.
Beyond these, Tucson is wall-to-wall Mexican restaurants and most of them are OK (but frankly, they all offer what is essentially Sonoran food that is not my favorite Mexican). One caveat--personally, I would NOT stand in line for the oft-recommended Mi Nidito (which is seemingly most famous because it's where Bill Clinton ate on a Presidential trip to Tucson). I find the food nothing special.
<message edited by BT on Fri, 03/11/11 12:43 PM>