What part of Austin, what are you looking for?
off the top of my head I would suggest in no particular order:
foreign and domestic
Russia house
Justine's
for a classic local flair :
Texas Chili parlor
Hut's
Casino el Camino
You will get a lot of suggestions and there's no shortage of good food in Austin but I would recommend Shady Grove. It's close to downtown on Barton Springs Road and every Thursday night they have good music on their "Unplugged" stage.
If you're talking about your classic WTC kind of place, then Jeffrey's, Perry's, McCormick & Schmick's, Trulock's, Fonda San Miguel. Blue Dahlia is pretty good, too.