This list comes from a very reliable Austin-based source. I will try to hit some of these up this weekend.
Lambert's: Best for Sunday brunch. Don't let the fact that they use gas fired smokers deter you.
Iron Works: Beef ribs. Great building.
The County Line: White tablecloth eatery. Along with The Salt Lick, the most recommended BBQ in town.
The best BBQs are actually in small towns surrounding Austin.
Lockhart, Texas (40 minutes south of Austin):
The owners of these two places are siblings who parted ways. Both have great sausage, pork chops, beef shoulder, and brisket.
Taylor, Texas (50 minutes northeast of Austin):
Louie Mueller's BBQ: Good sausage, brisket, and great beef ribs in a cool old building.
Spicewood, Texas (50 minutes northwest of Austin):
Driftwood, Texas (35 minutes southwest of Austin):
The Salt Lick: The most well-known. Unique sauce, known for chicken, Sunday prime rib. BYOB.