There is a large super market on the west side of town - I totally forgot the name, but it's where everyone in town as well as Americans shop. Just ask someone, "?donde esta el supermercado?" and they'll tell you where it's at. It's the only one.
It actually has a decent selection of everything you need, plus a good bakery.
p.s. If you need any more help, check into the Southwest board. That's where all of us Arizonans hang out. I'm actually interested to hear about your experiences down there. :)