There's a lot of great courses here in Austin. I'd spend a few days here if you can. A day at Twin Parks (36 Holes) (I think they have camping) and a day at Circle R (36) (I know they have camping if they're open) both west of Austin. Then Circle C and Manor both need to be played and you very well may want to play each of them twice. And you could spend a day playing Wilco (18), Brushy Creek (9) and Cat Hollow (Brushy Creek MUD)(18.) Pease Park is downtown and fun, though it can get crowded depending on when you try to play it. But an early morning round there and an early afternoon at Circle C would be doable. But if you wait until 3pm at Circle C or Pease, you're probably going to get backed up b/c they start to get some traffic.
Depending on the dates you'll be down here, Circle R may or may not be open. I know the Texan DGCRers are planning a Circle R round on April 17th. So that may be a great time to be here!
Send me a PM when you start to finalize your plans around Austin and depending on when you're around I can recommend eateries, etc.