6th Street is a college hangout area and last time I was there this past December it seemed like it was turning into a tourist trap of sorts. Don't get me wrong, you can definitely have a good time there, but as it is with most cities there are lots of other fun bars and nighttime attractions outside of this "party district" area that most visitors usually don't bother to check out. 4th Street isn't too bad but it's a bit ritzier. If you just want some dive-y, hangout bars, try heading up to the north campus area on Guadalupe. Here's a crash guide for some stuff do while you're down there.
If you want good bbq, the Salt Lick in Driftwood, a 30ish minute drive from Austin, isn't bad. Apparently there is a location in Westlake (one of the richer neighborhoods in Austin) but IIRC it's not the same as the original one.You can't also go wrong by taking a quick trip down US-183 to Lockhart and indulging in some bbq at Kreuzs (closed on Sundays) or Smitty's. If you have some money to burn and you want a good steak, apparently III Forks is excellent. I'm not sure if this place is still around, but the Hofbrau on 6th Street was always good for a reasonably priced steak during the day. A lot of people might tell you great things about Katz's Deli but it's a shadow of its former self. The prices have gone up and it seems their sandwiches have shrunk in size, same thing with Kerbey Lane Cafe. If you like chicken wings, try Pluckers. For Mexican food, try Maudie's Cafe on Lamar or Matts El Rancho on Lamar as well (they used to be closed on some oddball day like Tuesday or something.) Angie's right off I-35 on the east side is pretty good too.
For daytime attractions, you can go to the Barton Springs pool at Zilker Park (it's a natural spring and it's sometimes closed so check before going.) There is also the Hamilton Road pool on the outskirts of western Travis County. The Bob Bullock Museum is interesting too and IIRC there is a new art museum around the corner from there as well. Of course a visit to the state capitol is a must. The UT Tower, made infamous by Charles Whitman, should be open for tours but I think their hours of visitation vary according to UT's schedule. The LBJ Museum is pretty cool too. Mt. Bonnell has some cool views of the city on a clear day and it's a fun little drive to get up there.
The Longhorns have two home football games during your stay so if that's your thing, you can see if you can score some tickets. If you want to go on a road trip to indulge in some college football, go to College Station, a 2-hour drive from Austin. Kyle Field is a pretty cool stadium and College Station is a nice college town. The Aggies have two home games as well during your stay. If you like baseball, the Round Rock Express, the AAA affiliate of the Houston Astros have some home dates during your stay I'm sure.
Hope that helps! Feel free to IM
me if you have any questions. And anyone else with information about Austin, feel free to correct me on anything that isn't an opinion