Austin's really grown as a beer destination since I first went there back in the mid-90s. Back then, the only really good places to go were Waterloo Brewing at 4th and Guadalupe (sadly, it's gone now), and the Gingerman. Now there's so many you'll wish for more than four days.
Agree with Gingerman as a must stop. I'd also add my favorite--The Draught House (4112 Medical Pkwy). It's got a top-notch beer list. The food at Uncle Billy's was pretty good, as was the beer, so I'd agree with adding that to the list. There's a few local breweries, but I'm not sure what their hours are or if they have tap rooms--(512), Independence Brewery, and Live Oak Brewing Company are a three of them. You will probably find some of their beer at Gingerman, and Draught House.
Have a great trip.