My ex-girlfriend lived on 21st way south right around the corner, we ventured over to J Clyde all the time. Great selection and just a really cool place to hang out and hear some live music occasionally. Along with a great beer list, I recall that they also know how to actually make a cocktail.
While we are on the subject of B-ham bars, don't forget to venture around the corner to Marty's when everyone else closes up at 2. Some would say a dive, I would say a very classy establishment!