Check Whip In. That's where I've always got them. The last release was actually sent to stores as well (this is normally a beer that you can only get from a bar... and only to-go in bars that sell beer via retail [no liquor, beer/wine only]).
South Lamar is considered their "flagship" location. I personally go to Lakeline (and went to Slaughter when I lived South), but that's probably way out of your way.

Another option is Flix Brewhouse, which is a brewery/theater w/ food. Really good IPA there and it's pretty much an Alamo clone in most respects.
Pinthouse Pizza is slangin' the dankest IPAs in all of Texas right now.
Austin Beerworks is just a joy to go to and they always have exclusive beers on that you can't get elsewhere. Plus their taproom staff is #1 in my book. Their new taproom that just opened is one of the nicest in the city.
Check do512.com before you leave. It has a music schedule for each week downtown.
Keep in mind, because this is a production brewery, you can't buy beer on-site to-go because of our dumb laws. Spec's always has Live Oak for cans for about $7.99/6-pack though (sometimes $6.99 on the weekend)