Ok, so I've got five favorites.
Best of the Best TitlesIt's a tie, IMO, between a NY Style and a Chicago style place, since I like both types the same amount. IMO, one's not better than the other. They're just different genre's, really. You can't compare them... well, people do all the time, but I don't. They both rock.
Here they are, in the order of the time it took me to find them and try their pizza...
NY Style:Saccone's Pizza and SubsWeb site:
www.saccones.comMottos:Best Pizza in Austin
Pizza with a Jersey Attitude!
They're currently in two areas around Austin. One shop is in a little town called Leander and the other is in a section of Austin the city called Anderson Mill. The one I go to is in Anderson Mill.
It took me four years to find this place after I first moved here. First time I walked in the place, they had some memorabelia from home on the walls... Including a Shop-Rite sign poster, and of course Scrunchy was sitting on the cash register. I knew there had to be some good pizza here!

Man... the place rocks. It's just like the traditional NY pizza I grew up on. It better be, 'cuz the guy that owns the place is from Jersey (Carteret). If his family ever found out he was making pies that didn't taste legit, I'm sure Sully and Vinnie would be payin' this guy a visit in the middle of the night to fit him for some concrete shoes...
They seriously make a knock-out of a pie.
My favorite specialty pie is the one they add a few basil leaves and lots of cracked black pepper to. ("Mom & Dad's Special")
They're a little pricier than I remember pizza being back home, but it's probably because they have to 'import' their ingredients from The City.

LOL
Chicago Style:Mangia Chicago Stuffed Pizza
Website:
http://www.mangiapizza.com/Motto:Stuffin' Austin since 1988!
They have four locations around town. The one closest to me is the Gracy Farms location. I'm starting a grass roots campaign to get them to open one in Anderson Mill, but we'll see how that goes.

Try the Carnivore! Dude... it's awesome.
Their's is the best Chicago Stuffed Pizza I have ever had.
A little Expensive, but you get your money's worth and then some.
~~~
Runner ups:Rockin' TomatoNot quite NY Style... Pizza is more like a crackery kinda crust.
It's good.
Gino's in Round RockVery close to NY Style, but not quite.
It's very good
Reale's Italian RestaurantAlso very close to NY Style, but not quite.
It's very good, but more expensive than them all, except Mangia.