6th St is a great place to get a drink and listen to some live music. It's a hangout of University of Texas (U of T) students, so it's always a lively atmosphere.
6th St really turns on around 7pm but livens up around 10:30/11 and doesn't stop until well into the night.
The mecca for anyone who has ever sampled Shiner beer. You can enjoy Shiner Bock, Hefeweizen, Lite, Summer, etc. It's an interesting tour and a magical place.
It's also an hour and a half waaaay outside of Austin, but well worth the ride.