1)If your up for a little drive, the Salt Lick located south of Austin in Driftwood, has the best damned BBQ anywhere (in my opinion). But make sure to bring your own beer since the county is dry. Also, bring cash, they don't take credit cards.
2)Another uniquely Austin eatery to check out is Hudson's on the Bend. The restaraunt is a little pricey but the food is out of this world. The menu features dishes including venison, boar, and quail.
3)If your into seafood (yes you can get good seafood in Austin) check out Eddie V's Edgewater Grill.
4)If you want a really casual dining experience, try Katz's Deli on 6th street. This is an authentic New York Delicatessen.
5)For tex mex, nothing beats Matt's El Rancho. Although I am a big fan of the Chicken Mole Enchiladas at Guero's Taco Bar.