As is the case with many of my visits to college towns, my most recent trip to Austin took place in conjunction with an academic conference.
Like Madison, Wisconsin, featured in my entry immediately prior to this one, Austin hosts a huge, state university flagship campus, the state capitol building, and state historical society/museum. Pictured below is a collage of the famous Texas Tower from the UT campus, the Texas capitol building, and Texas State History Museum, all located in close proximity to each other.
Downtown Austin and environs have a lot going on, all within walking distance (if you like a good walk). Austin is the self-proclaimed "Live Music Capital of the World" and home to the PBS music show Austin City Limits. Many visitors will want to go into some of the clubs on Sixth Street, but it's fun even to just walk up and down the blocks, which allows you to hear a new band's music coming out the front door every several seconds.
Another great thing about Austin is its relatively new airport, converted from the former Bergstrom Air Force Base. It's one of the most attractive airports I've ever seen, and has plentiful shopping venues, all, I'm told, based in local businesses.
[UPDATE: I visited UT-Austin again in 2009 and have some photos of that trip.]