Tough being a public player in Austin, because the only courses close in are private clubs or munis (although for munis they are pretty good).
Private clubs in descending order of cost/exclusivity:
Austin Golf Club (C&C)
Austin CC (Dye)
Barton Creek Resort/CC (Fazio Foothills, Fazio Canyons, Crenshaw Cliffside, Palmer Lakeside)
Hills of Lakeway Resort/CC (Nicklaus x 2, and 2 other resort courses)
Onion Creek (Demaret)
River Place GC
Great Hills CC
Balcones CC
Lost Creek CC
New clubs are going in SW and W of town in the hills; stay tuned.
Public courses:
Circle C Ranch (Morrish)
Munis (Lions, Clay/Kizer, Hancock, Morris Williams), Riverside
The Barton Creek courses are good (esp. Fazio Foothills), Austin GC is supposed to be great, Austin CC is very hard but good, Circle C is good, River Place is way too tight to be fun, Lost Creek is tight but fun, Onion Creek is solid, Hills of Lakeway (original Nicklaus) is good.
Horseshoe Bay Resort (RTJ) is an hour away with good courses and scenery (and high prices). Colo Vista in Bastrop is a strange and good semi-private course. The Bandit (Keith Foster) in New Braunfels is quite good. Delaware Springs (Axland & Proctor) in Burnet is good. Mill Creek (RTJ, Jr) in Salado is solid. And San Antonio is 1.5 hours away with many more options.
If you are a public player, be prepared to play munis and Circle C or put the miles on your car.