Don't leave Austin without a trip to the Oasis. Live music, beer, and the most amazing views in TX.
There was a fire there recently, but they've re-opened.
http://www.oasis-austin.com/
it's so nice there, I'd actually venture out of South Austin.
Another great run is the restuarnts along Barton Springs Road. Chuy's is world famous for it's cuisine and a litttle incidnet with a Bush Girl.
http://www.chuys.com/
Finally, you can't beat Threadgill's. I know that the Northside is the first, but the world headquarters on the Southside cannot be beat (escpecially since you're coming from the airport). The Sunday gospel brunch is one of my favorites:
http://www.threadgills.com/