Sweetwater IPA and 420, and red hare national common are the only ones I remember seeing and the Common is only at Holman and Finch burgers
I have seen Hopsecutioner cans too. Draft options are terrible. GI IPA is about the only one remotely drinkable. I have been served out of date SW IPA in the past. The beer sucks as bad as the team for sure.
I don't think Sweetwater sells it, but Frozen Pints (beer flavored ice cream from GA) is represented there.
I used to when the Phillies were in town, the beer options aren't all that great especially tap offerings. The food options arent that much better either. The nice part if you have kids they let you hang around the dugouts during BP to get autographs. In contrast in Philly if you don't have tickets to be there the ushers chase you out. If your new watch were you park, roads are one ways after the game. If you need to get out 20 east the orange lot is good. If your 85 north the green lot is good.
Just FYI on food -- http://atlanta.braves.mlb.com/atl/ballpark/information/index.jsp?content=security "Food, drinks (non-glass, non-aluminum, non-alcoholic) and soft-sided coolers (with the plastic liner removed) ARE permitted. Beverage containers may also be subject to inspection." I always bring in a few CFA sandwiches and drink Yuengling tall boys.
If there was anything close to Turner in the way of a bar I doubt it would be safe. Not a place I'd walk around looking for a beer.
It may look sketchy, but it's really not a bad neighborhood. My boss lives four blocks away and we've walked plenty of times to and from the stadium, usually after a night game. Not a single murder has occurred. I second Augustine's. Solid food, best beer list in the area.