There are a few hotels just east of IH35 that are very convenient to UT. They're major chains, though I can't remember their names right now. Downtown is just south of campus, so you could stay at any hotel there and either drive or take a cab to campus. If you drive, you can park in the LBJ Library parking lot on Red River, north of Martin Luther King Blvd (MLK), and the library has some interesting artifacts, so you might enjoy a visit. I'm assuming the audition is music, and the LBJ Library is close to the music building (relatively speaking--this is Texas). UT also has some museums (Texas history and art). Check out their Web site to see what's going on as far as exhibits.
Restaurants and things to do depend on what you like to do and eat. There are plenty of restaurants in the area. Just give us a heads up as to what you like.
If you're into performing arts, check out UT's site to see what shows, dances, concerts are on for that weekend. Also, spend some time on the UT campus. Check out the South and West Mall areas, and take a tour of the UT Tower, if it's open. The campus has some great landscape and architecture.
If the weather is nice, and you have a car, you could head out to Zilker Park and walk the hike and bike trail along the lake. It's nice on the weekends, especially on Saturday mornings if the rowers are out. The Botanical Gardens are also on Barton Springs Rd. across from the Zilker Park entrance. If you like Zen-style gardens, this is a nice place to spend some quiet time.
If you like shopping, check out SoCo (Congress south of Riverside) for some eclectic shops reminiscent of old Austin. We also have a few malls and some interesting stores at 6th and Lamar (where the Whole Foods mothership and Book People are). You can also walk "The Drag," the street just west of UT campus that is home to some bookstores, clothing stores, and eateries. If your daughter is going to UT, she'll become very familiar with that area.
If you have any special interests, let us know. I'm sure others have suggestions. Have fun!