Houston1836 makes a good point about do you want to stay at a resort when you're not going to get a chance to enjoy its services?
Traffic Sunday AM will be no problem. You should think about staying in Austin. From central Austin, it should take you 20 minutes to get to the airport, and another 5 - 10 minutes to turn in your rental car. (If it's real early, then less than five minutes since you just drop your key in the box.)
However, if you really just want a place to stay overnight, then stay at the Airport Hilton. The Hilton has a little bit of history as the former headquarters of the old Bergstrom Air Force Base that closed several years ago (and became home to our "new" airport.) It is apparently something of an architectural wonder -- a round building with a courtyard (that has since been turned into an atrium).