Although I live in Houston, I do know Austin fairly well. Sixth street is ok, but for the real fun hit up 4th at night. Much better drinks, bars and people. For bars I would suggest Cedar Street Courtyard (at 208 W. Fourth Street).
For resturants check out Romeo’s (at 1500 Barton Springs Rd and has great Italian food) or Shady Grove (at 1624 Barton Springs Rd where the Austin Dopefest was held).
If you feel up to a movie try the Regal at 901 Little Texas Lane in South Austin. Wonderful theater. Modern looks with an old school feel.
If your up for a walk, go down to the drag on Guadalupe street. This is the southern edge of UT and is filled with shops, resturants and the counter culture of Austin. Not to be missed, but hit it during the day.
Being a touritsty type of person I won’t feel right unless I say see the Texas State Capitol at night for yourself. The pink limestone and beautiful architecture (all built by Texans with materials found in Texas) is not to be missed. Depending on when you come in, you might be able to hit South by Southwest or Mardi Gras. Do not miss these if you have the chance.
Hope this answers your question!