Sprouts is probably the best place in the East valley to get most of your groceries. Their produce is fresh and the prices are excellent. Seriously, buying stuff at Sprouts is cheaper than buying at CostCo, and you don't need to buy 500 pounds of everything you want. For example, today I got 5 pounds of yellow onions for $1 and 10 pounds of russet potatoes for $0.99. Their spice section is excellent too as you can buy bulk spices - if you need a tablespoon of an obscure spice for a recipe, you can just buy a tablespoon for 25 cents instead of buying a $10 jar that will mostly just go to waste.
Sprouts also has very fresh meat and seafood. They have a decent selection of fish - I get ahi tuna steaks here and they're quite good. Sprouts also has a huge section of various kinds of fresh sausages which are giant and fantastic.
Since Sprouts is a Farmer's Market/Organic type place, there will be some things that you can't find here and will need to go to a "normal" grocery store for. Not to worry - there's a Fry's just across the street on the Northeast corner of Ray and Dobson.
If you shop here, you will save a *lot* of money compared to shopping at other grocery stores and you'll probably end up with fresher food, too. So check Sprouts out sometime - you'll be glad you did.