I live in Austin. If you want to have a good night and get a bunch in all at once:
1. Iron Works BBQ is in DTWN and as good if not better than almost all the others. Salt Lick you have to go to the original and most of the other amazing one's are all a long trip.
2. Rainey St. Go. So many different bars and everyone can find something that works for them
3. West 6th Street, about half a mile from Rainey and is the original place to go in DTWN Austin. I'd suggest Rustic Tap but if you want something a little more exciting then good beer and live music just up the street are three great spots on the same corner (6th and Nueces) Star Bar, Parlor and Yard, and Little Woodrows.
The Domain was mentioned above and is a great spot for an afternoon drink with shopping and dinner. Velvet Taco if you are up that way is a favorite of ours. It's a long way from downtown though. It really all depends on where you are staying, how long you are in town for, and if you have a car. If you make the trip to SA go to "the Pearl". you're welcome.