You will need to go to brewpubs to get food and beers that are made onsite. Here in TX, full on breweries (512, live oak, real ale, etc) cannot sell on premise if they are distributing elsewhere (bars, stores, etc). Some have sample rooms, but they are usually minimal since they can't sell. I know in other states you can go to a brewery and get beers, food, merch,etc and have a great experience. Hopefully this will change.
Brewpubs on the other hand, can sell on premise, but cannot distribute.
Why mention this? To lower expectations of getting to a full on brewery around NYE. You will have to stick to the brewpubs, or straight up bars to get a sampling of local beers.
With that said:
Blackstar COOP: House beers, solid guest taps including texas beers and some micro's and menu featuring 'texas pub fare'. Menu has lots of local ingredients, vegetarian, etc. Reasonably affordable. My first choice for balance between good food and solid beer selection.
NXNW: Only house beers which are well made, but don't get too extreme (their pale ale is great though), and the menu is a bit fancier and pricier.
UncleBilly's: Good House brews, some local guest taps. Barbecue/food is not good.
Draughthouse: Few food options, but the reason to come here is to drink quality craft brew. This is my favorite place to drink beer in austin. House brews are always changing and is not the focus of the bar. They have 60-70 taps, and 2-5 of those will be house beers.
To answer your q: I would go to Blackstar to get fed and have a few house beers. Once done there, I would cruise down the road and have more beers at Draughthouse. If you have more time here, then I would hit up NXNW and maybe Uncle Billy's (for the beer).
Black Star Coop: http://www.blackstar.coop/
This cooperatively-owned-and-operated brewpub has a menu that surpassed all of our expectations. You can get your standard pub grub there, but they have a lot of other interesting and delicious things, too. It's an easy place to get to (and to park), located at the intersection of Airport & Lamar. It's also on the MetroRail at the Crestview station if you won't have a car during your visit.
Black Star Co-Op Pub & Brewery
7020 Easy Wind Dr #100, Austin, TX