New York Style Pizza in Austin
While Texas is probably better known for Barbecue and Mexican Food, there are some places you can get pretty good New York style pizza from independent restaurants.
Probably the most popular place for thin crust pizza is Home Slice (1415 South Congress). They serve hand tossed pizza by the slice or the pie. You can do dine in or carry out, but they do not deliver so be ready to drive down to SoCo if you want your fix.
Salvation Pizza (624 W 34th) is also very popular. A lot of people have a love / hate relationship with Salvation. They love the pizza, but the service is not known for being top notch. When you go be sure you have plenty of time. There are stories of 15 minute waits for drink orders. They are closed on Mondays.
Rounders Pizzeria (1203 W 6th St) is not my favorite place, but a complete article means I should mention them. I thought they were expensive for the quality of pizza you get. If you are driving there keep an eye out. It easy to miss the turn in and you will have to do a loop on one way streets. They do have a limited delivery area. They do not always deliver to campus, however.
Southside Flying Pizza (2206 Congress) is probably best compared to Home Slice since they are a stones throw away. They are slightly cheaper but they also use slightly cheaper ingredients. There garlic bread is universally praised. I also hear a lot of good things about their Caesar Salad.
I have not gotten around to trying East Side Pie (1401 B Rosewood Ave). The people I have talked to swear by it. I have not seen people this excited about a new pizza place since Home Slice.
Hoboken Pie (718 Red River St) is also an exciting new pizza place downtown. Its not something I am looking for, but they serve vegan pizza. They also will apparently deliver to bars downtown. I have not tested this myself, but it sounds awesome.
These are the places I know about. Please contact me if you know of any others. Also feel free to use Yelp.com so you can read other people reviews about these places. Good Luck and enjoy your slices.