Blue Adobe Grill is one of my favorites in town. It's New Mexican style, but not as spicy as many other New Mexican spots (such as Los Dos Molinos, which is excellent but verrryyy hot). Mango's, on Main in downtown, is a great spot for lunch...I love the chips. Rosa's Grill is another decent spot that does basic Mexican fare well (and their salsas are wonderful...esp. the sweet verde salsa).
I've added links, but there doesn't appear to be one for Rosa's. Here's the Yelp page: http://www.yelp.com/biz/rosas-mexican...
Los Dos Molinos
260 S Alma School Rd Ste 137, Mesa, AZ 85210
Mango's Mexican Restaurant & Bakery
44 W Main St, Mesa, AZ 85201
Blue Adobe Grille
144 N. Country Club Drive, Mesa, AZ 85201
I'll add two to the above suggestions:
Chileros is some pretty good stuff. No liquor license, but good caring service. A little hard to see from the road - just north of the Bascha's in the same strip mall.
Avoid Nando's (on Mcdowell and Power) like the plague. Truly, a weight watchers frozen mexican entree is better.
I've also added Red, White and Brew. While it's not Mexican, I think it has some of the best food for the price and service in the area. The menu is wide and varied and very good, servings are large, so expect leftovers. Excellent service, no reservations, may have to wait for a table, esp. on weekends.
I'd also suggest you venture a little bit and go to Los Sombreros. Not very far into South Scottsdale and will likely be the standout meal of your trip if you are concentrating on Mexican.
Los Sombreros Cafe & Cantina
2534 N Scottsdale Rd, Scottsdale, AZ 85257
Red White and Brew
4580 S Gilbert Rd, Chandler, AZ, USA, Chandler, AZ
1157 N Ellsworth Rd Ste 101, Mesa, AZ 85207
Mariscos Sinaloa at the corner of McKellips & Gilbert is great for Mexican seafood and not too far from your location. Not a lot of English spoken, but that lends to the fun of it.
My favorites are the 'chicarrones' (fish), coctel de camaron or mariscos, huachinango filet (done in your choice of styles - breaded, broiled, veracruz style, and several others) and camarones al chipotle. Husband loves the arroz marinero (with a variety of seafood). Most entrees are served with a side of rice, salad and sliced fried potatoes. Service can be slow, but very friendly.