AJ's is a fantastic supermarket. Don't buy your staples here as you will do better at the other chains. AJ's is strictly high-end meat, seafood,cheese, wine, deli, bakery.
The wine selection is the best you will find in any Phoenix metro area store and the beer selection is equally as good. if they don't have it, ask and in most cases they can get it for you. The meats and seafood in awesome. Prime cut USDA aged beef, quality seafood..however its pricey.
They also have cigars as well as a great flower shop. If I haven't planned for Valentines day AJ's is the one stop I make on my way home.