I moved to the area not so long ago, so I've tried a few places. The list on this site probably won't result in a wrong turn:
The Essential Barbecue Spots in Austin - Eater Austin
The ones I tried were Terry Blacks, Stiles, and Rudy's.
Terry Blacks: Perfect amazing brisket, good sauce which you just squeeze out at the table, fairly good sides but nothing amazing
Stiles: Slightly less perfect brisket than Terry Blacks, a little bit heavier seasoning, amazing/perfect clearly homemade sauce given with meat in a sauce container, best sauce, though somewhat more expensive sides. Area isn't bad, but it isn't the best area in town. I took the unused sauce back home and used it again with another dish and it was great.
Rudy's: Disappointing, in all ways. Went because it was nearby and supposedly had OK ratings. The dining style is basically the normal one at most BBQ places, nothing special, the outdoor 3-season eating room was a bit interesting, this was the one good point. Extremely corny 1st time customer greeting, basically like having someone suddenly sing you happy birthday in a restaurant, and make you never want to go there again. Brisket was bad, not juicy, something frozen and heated in the oven would be better. Sides were ordinary, not bad though. The sauce, ugh, this is the exact opposite of Stiles. It is the worst sauce I've ever had in my life. You can use the dispenser to use as much as you like, or buy a big bottle of it, but when you look at the ingredients you realize, this is just a big bottle of HF corn syrup, which is disgusting in BBQ sauce. My parents went as well and really didn't enjoy it either.
