BE's tips are good ones. The first highlight would be Franklin. Enough has been said about it -- all true. Take a short trip to Lockhart (about 20 minutes from the airport) where you should at least stop by the Big Three: Smitty's is a piece of Americana you won't find anywhere else, Kreutz is a classic and Black's has an amazing beef rib. They are all close to each other and the courthouse is an classic bit of Texas architecture. The Salt Lick is a great experience -- a huge rustic camp in the middle of nowhere, but just about 30 minutes from downtown Austin in Driftwood. The sausage is great. Bring your own cold beer and just order the meat by weight -- the sides are not so great. The pecan pie, however ... Cooper's has several locations but the original Llano joint is best. It's a hike out Hwy 71 from Austin, but the pork chop is worth the drive.
While you're down here, take advantage of the awesome music venues. Highlights: Dale Watson, most Thursdays at the Highball on S. Lamar, Redd Volkaert for Saturday Happy Hour (3pm; free) at The Continental (South Congress), Chickensh!t Bingo on Sunday afternoon at Ginny's Little Longhorn on Burnet. Take in anyone's show at The Broken Spoke on S. Lamar. The definitive honky tonk. Stay off of Sixth Street. If you really want a laid-back Hill Country experience, go to Luckenbach on a weekend afternoon, after first having lunch at Cranky Frank's in Fredericksburg. It's a good hour-and-a-half from Austin, but it's a nice ride through Texas wine country (yes, Texas wine country).
Hope you have a great trip!