Meh...I'm not really all that fond of the cuisine @ the Oasis. There's another restaurant to the right of it,
www.soleilaustin.com that has better quality.
If you guys like Thai, you should try
http://spinmodernthai.com/ They have very few staples on the menu, with everything else rotating every 2 weeks or so as they try new things. The former head chefs @ Uchi and Uchiko are the culinary chefs there.
Downtownish off Lamar, if you're feeling like a little cajun, I'd recommend Shoal Creek saloon,
http://www.shoalcreeksaloon.com/. They have an *excellent* chicken fried steak and gumbo. Be forewarned, it is a Saints-themed place.
You'll also need to get some bar-b-que while you're here. I'd recommend Franklin's
www.franklinbarbecue.com/, but the line is LONG, EVERY DAY *lol*. Everyone seems to enjoy Salt Lick a little south of Austin
www.saltlickbb.com, but I prefer Rudy's smoked turkey and cream corn
www.rudys.com 
You can check out the reviews of any of those places online.
Have a great stay!