The Gingerman downtown is my fav:
It has a great atmosphere, awesome outdoor patio under some oak trees, and a massive selection of beers.The inside is all dark wood, comfy chairs,
a pool table or two. It will be moving to a new location soon, but that's just a few blocks from where it currently is, and I've talked to the staff who say they're going to keep things as close to the original location as possible.
The Flying Saucer is another great one. More polished place, and often packed to the gills. The beer list here is also somewhat astounding. They have good patio seating, as well.
The Draughhouse is also something pretty special: On top of the huge outdoor patio area, people can (and do) bring lawnchairs, sit in the bed of their trucks etc, in the parking lot. I have no idea how that can be legal, but it's been going on for a long time. A very cool atmosphere.
The summers here are very hot, and run from around march - oct, which means outside of nicer places you'll frequently find lighter beers, lagers, etc. Beloved for some reason are Lonestar and Shiner Bock. Shiner is potable and beats drinking water. That's all I'm gonna say about those. All of the better breweries seem to offer a good pale ale or IPA thankfully, and experiment frequently with other types as well.
Microbreweries are becoming more numerous in Austin pretty quickly. I've heard that the moonshine laws that prohibited homebrewing were more recently changed in TX than other places so TX folks are playing catchup a little. However, they're doing a good job. A few of the good ones that come to mind:
North By Northwest (brewery restaurant): http://www.nxnwbrew.com/
Real : http://www.realalebrewing.com/
St Arnolds: http://www.saintarnold.com/
(512) Brewing Company: http://512brewing.com/
Independence Brewing Company: http://www.independencebrewing.com/ about 9 years ago
I recommend Steve's reply. It's great. The Gingerman is the best place to throw a few back in Austin and in Dallas.
Chances are, you've had a Shiner in the past. Shiner's my default, and the greatest TX beer. Shiner's variations don't match the real thing. almost 9 years ago