I can't go near central Phoenix without a visit to Baiz Market. They have everything from fresh baked pita bread to string cheese to Middle-Eastern pastries to a full grown grocery and meat section. Their selection includes foods from the Middle-east, Europe, Africa, and Asia. There has yet to be a spice that I have not found there.
My favorite part is the small cafe with fresh food and loads of garlic. You can watch your food being made and pulled from the hot oven. I've had just about everything but my top recommendations are: chicken shawarma, falafel, and manaeesh (both the za'atar (thyme) and cheese (jubna) varieties are excellent), I have not tried the meat version.