Hi,
Dont know if this is too late for you, but as you did not give price range...here is an assortment. First, UT does not have too much super close - but downtown is not far and has some great places....
Austin Motel - quirky-fun-hip-super reasonable-not too fancy, but celebrated by locals - located near downtown - people love this place and you cant beat the prices if you can get in. They are always
Four Seasons - on the water or with city view - more pricey but very nice - happening bar at night and fabulous Sunday brunch
Driskill - right on 6th Street - a very fun place - mid range - a classic
Omni - also in 6th Street vicinity - nice - more business folk, but still location is good
Those would be my top 4 and places I have stayed. They are all online so you can check them out.
Good luck, have fun! Let me know if you have any other questions!
Michelle