Not just because I'm a chef there, but Jasper's. Seriously, we do happy hour open to close EVERY day of the week. $5 appetizers and specialty martinis and $2 off all liquor, beer, and wine. One of the best in Austin!
Jasper's is always a good choice at the Domain. I've also heard good things about Sam's Boat, off of MoPac & Breaker. Just moved to that area so I'll be giving them a try soon.