Our fellow 'hound sambamaster is leaving Austin for Wichita, Kansas, on Tuesday, yet his favorite restaurant, Asia Cafe, is closed this week. I don't know how many meals he can cram in before he leaves, but I think we can all agree that every one of them should be amazing.
Sambamaster's posts indicate that he considers all Italian food in Austin to be quite bad. The only Mexican/Tex-Mex I've seen him consistently praise is the chow at La Michoacana Meat Market. Plus, he favors the cooking of honest, unpretentious chefs over that of many graduates of fancy cooking-schools. So, let's leave off the usual suspects, for his sake.
Off the top of my head, I'll make one suggestion. Don't leave town without trying the tacos bañados at La Regio Montana. This is a drive-through on East Riverside, so you can get several plates to-go and still have plenty of time to pack. You may as well order a campechana and a tostada Siberia while you're there, plus some Mexican coke to wash it all down with. And ask for some of their green salsa made with just emulsified crema and really hot chiles. This thread has more details:
What other suggestions can we come up with, chowhounds?