I'll second Antones and La Zona Rosa for the music. Walk down East 6th street and you'll hear a few tunes, too.
May 3-4, 2008: 29th Annual Pecan Street Spring Arts Festival. Pecan Street is 6th street.
My Favorites: Rudy's BBQ; County Line on the Lake (BBQ); Hut's Hambergers; Threadgills (comfort food); Fonda San Miquel (interior Mexican); Gumbo's; Chuy's (TexMex); Reale's Pizza & Cafe (Italian); Antonio's (TexMex); Hula Hut; Maudie's (TexMex); Mangia's Pizza.
If you want to travel a bit: Saltlick (BBQ in Driftwood); Louie Mueller's (BBQ in Taylor); Cooper's (BBQ in Llano); Hudson's on the Bend (wild game/exotic ingredients near Lakeway)
Things to do:
-Rent kayaks on Town Lake (now LadyBird Lake) and see downtown from a different perspective
-Bob Bullock Texas State History Museum & Texas Capital
-LBJ Presidential Library on the UT campus
-6th Street at night
One final thing about the food: Austin has more home-grown, one-of-a-kind restaurants than almost any place on earth. Tell me what you like, and I'll give you a few ideas.