there are a few different answers for this depending on the person & the area, but if you do a quick search for "Columbus" in the title of the thread, there are several pages of other threads where this has already been asked & might get you answers quicker than waiting for everyone to chime in here. personally I tend to pretty much only go to World of Beer - Easton, because it's the closest thing to me. Weiland's is great. The Savor stores have good selections but a bit of a history of sketchy business practices. Crest has a great selection & happy hour (food is also good but a little overpriced).
Two years ago, the answer was unambiguously Bodega. Now, it's a bit murky. Most bars update on beermenus, so start there. by area: An easy, fruitful stretch along Indianola in Clintonville is - The Crest - bar, good food Studio 35 - awesome movie house with an attached bar, with always a killer taplist Savor Growl! - bottles and drinks Palmers - underrated bottle shop Weilands - bottles and growlers, too popular so best stuff goes quickly I like to grab a growler from Savor or Weilands and go to Cafe Bella on High, which is BYOB. short north Bodega (more off-brand Ohio than high rated beers, I'd say at this point) Pies and Pints Short North (on list bc next door to Bodega, usually has good cincy stuff and a FFF or two) Pint Room, full of bros and a long, uninspired list St James, off High, but awesome bar, usually has some Bodhi or so, well priced Old town east - Yellow Brick - cool pizza and great tap list, upstairs is arcade super awesome, which has great beer and is appropriately named
Really depends on where you are staying. I usually find WOB to be quite overpriced. Example: $12 for a 10 oz. pour of Rodenbach. With that complaint out of the way: Winking Lizard usually had a good tap list - food is regular bar food. 101 Beer Kitchen 2 locations - List is small, but usually can find something of interest - food is usually very good. The Crest Walrus The Pint House The Pint Room Daily Growler either location - make sure to go during HH. The wife and I have also enjoyed Land-Grant Brewing, Zauber, Zaftig (high gravity only, well as high gravity as Ohio's stupid ABV law allows).
In New Albany you're closer to Crafted Drafts (Store), and World Of Beer at Easton. But not too far away from the Short North, or downtown, which is where most of the places mentioned above are. I would also recommend House Beer, on N. High Street. It has a small, well curated draft selection, with hundreds of bottle/can options available for there, or to go.
I work in new Albany, I choose to hit wine and brew emporium on sunburry rd over crafted drafts typically. With that being said, check both out if you have time. B spot on Hamilton rd tends to have decent drafts but pies and pints Easton (get wings omg), or WOB Easton are def your best places to drink close by.
And last but not least, is Bob's, the Cultural Hub of the Midwest (TM). They have a good, often great, beer list, the falafel from next door is great, and for whatever reason, everyone there is on a mission to get sh*tfaced. Don't drive if you're going to Bob's.