Hopi.beer is one of Georgia's few beer retailers, as well as one of the only places in Batumi that you can find craft beer bottles and takeaway drafts. They stock a nice variety of beers, including the local Batumi Beer, NaturAle, Underground Microbrewery, SeaHorse, and Bayo. There is also a decent selection of imports, both craft and macro. The selection seems to change fairly often, but the emphasis on craft beers is very nice to see when most beer shops seem to tack on one or two as an afterthought to their macro selection.
You can visit their location in person to get takeaway beers, or pay 3GEL for delivery throughout Batumi. Their website works quite well, though opening it in Chrome and using Google Translate may be necessary for English speakers.