Will be there Wednesday night - name says it all - whatcha got?
I haven’t been there in awhile, but for brewpub I’d generally go to Blackstones or Boscos (brewpubs). Yazoo (brewery) has a taproom open Thurs-Sun. The Flying Saucer would be the place for the widest variety of beers (although probably not so much for local brews).
There is a place I have not been called 12 South Taproom and Grill. It sounds like what you may be after.
I think that is about it…
I haven’t lived there since 2005, but MDixon named all the places I remember going. I’ve heard that Yazoo has gotten a bit lazy, i.e., “pedestrian” in their offerings over the years. But Boscos and Blackstone have solid lineups pretty much all year round. Both offer cask beer on weeknights. In the interest of candor, I worked at Boscos for three years in college. 
Flying Saucer is a great place to sample just about anything. They’ve got over 100 tap beers and more in bottles.
Last week I had a beer named “Sue” that I think was from Yazoo. It was a smoked Imperial Porter. Certainly not pedestrian.
Plus it got me singing Johnny Cash all day.
I’m gonna call that smoked Imperial Porter Bill or George – anything but pedestrian! 
There’s a bbq place called “Puckett’s Grocery” off Broadway. We found it on our last trip.
The BBQ is good, the sides/specials as well - and its really affordable for that area. Best of all, they have a well-curated tap list of local and southern brews you don’t see if you live north of the Mason-Dixon.
I was also impressed by the beer knowledge of the staff. When I asked about one of the taps, the bartender happily poured me a few free tasters and was excited to talk beer.