My favorite pizza place in Memphis was Bosco's. It is more of a Roman style pizza with a thin crisp crust, and is definitely not in the Neapolitan or New York style, but none the less it is really good. It is cooked in a wood-fired oven, and had really top of the line ingredients. The "Palermo" is my favorite with sun-dried tomatoes and home-made sausage containing a good amount of fennel. The rim of the pizza is fairly wide but still thin, and the pizza is served with olive oil so that you can finish off the crust with the olive oil. It's not your normal style of pizza, but like I said, it is really good.
Bosco's is also famous for their beer (goes great with pizza). They were one of the first brewpubs that opened before brewpub mania spread across the nation back in the late 80s. Bosco's is especially known for their flaming stone beer. A couple hundred years ago there were areas in Germany that came up with a novel idea for heating large amounts of beer wort. Instead of building a huge system to heat a large vessel of liquid they heated some volcanic rocks and dumped those in the beer wort. These rocks heated the wort and also caramelized the sugars in the wort. A very unique way to cook beer, and Bosco's revived the technique. They also feature "real" ale that uses air instead of CO2 to dispense the beer, and the air interacts with the beer changing the flavor of the beer as it is dispensed. With this style of beer you get the opportunity of tasting the perfect pint where air has imparted a wonderfully unique flavor profile.
I also highly recommend Fino's Italian Grocery. No pizza there but their sandwiches are the BEST Italian sandwiches I've ever eaten -- and I now live only a block away from Federal Hill in Providence, RI. The one made with the olive dressing (I think it is called the Fino) is especially good, but their sausage sandwich is oh so good as well.
Lastly, my vote is for Corky's.