Publix can have great beers or they can have just the typical ones. I've seen some with 6 packs of Stone's Ruination IPA and Spaten Optimator, among others...most of them dont carry that kind of beer though, no idea whats up with that. Rogue Dead Guy Ale is at most of the Publix I've been to, that would be a decent choice (although not super cheap). Total Wine is pretty much the best place in FL to go shopping for beer, no idea if one is near you or not.
I actually just went to the Cigar City brewery on Saturday, was pretty cool. Still so small scale, the bathroom for the bar they have is in the middle of the brewery with a bunch of wheat and hops and shit just laying around, was awesome haha. Had a couple decent beers, need to go back and get properly acquainted sometime soon.