Basically, stick to High Street (or a block or two either direction off of High). It runs basically from south of downtown, through downtown, into the Short North, and up to Campus, Old North Campus, and then Clintonville. If you are coming in for just a weekend, basically sticking with German Village -> Downtown -> Short North.
Here is a quick guide I made starting from German Village and heading North. It basically just focuses on drinking (mainly brew pubs for local beers), but there will be plenty of other bars around these to check out too.
German Village/Brewery District is mainly neighborhood bars scattered around, but there are a couple bigger places. Columbus Brewing Company is about 2 blocks away from High (525 Short St Columbus, OH 43215http://www.columbusbrewingco.com/). If you want to go here, I would go there first as it sits down the hill by itself, and they do not stay open late, then you can walk back up to Front St or High St) There are a couple more bars right around there. World of Beer (503 South Front Streethttp://wobusa.com/Locations/BreweryDistrict.aspx) is next door. I would make anyone from out of town go to Double Happiness/Fresh Street (across from the WOB, about a block north) for yakatori. Double Happiness is the bar (482 S front St http://doublehappinessohio.com/) but Freshstreet runs their kitchen (https://www.facebook.com/freshstreet ) They serve till midnight, delicious Japanese style meats on a stick. They also have soju (Korean moonshine). Check their FB page first for hours they are serving, as they can vary from day to day.
Then you can get on High Street and walk about 15 minutes north through downtown. Or, get a cab, won’t cost more than 5ish dollars. Head to Elevator Brewery and Draught Haus (161 N High Str. http://www.elevatorbrewing.com/) to start. then walk back north a couple blocks to Barleys Ale House 467 N. High St. http://barleysbrewing.com/).
From there, you can walk north through the Short North, plenty of bars and restaurants to check out. If you have any wine drinkers with you, then they can venture north up to Camelot Cellars (wine- 958 N. High St. http://camelotcellars.com). Mouton (954 N Highhttp://www.mouton954.com/) is right next door if they want an olde timey craft cocktail and small charcuterie plate. Brothers Drake Meadary (mead- 26 E 5th Ave- set back from the corner of High and 5th http://www.brothersdrake.com/also this is attached to the Middle West Spirits distillery so they will have all of OYO’s different liquors http://middlewestspirits.com/). This is a must for anyone in my opinion. Good mead, great vodka and whiskey. North High Brewing is also just half a block up High Street from there (1288 N High St. http://www.northhighbrewing.com/), some really good beers there.
So, just copy and paste this to an email to yourself, then you can pull your phone out while you are out. You can tailor based on where your hotel is and what not. And if you want any restaurant recommendations, I am sure we can give you those too. And if you are over brew pubs at any point, there are plenty of bars to just drink on High Street.
Oh yeah, and Seventh Son (1101 N 4th Street https://www.facebook.com/SeventhSonBrewing?fref=ts ) is a great new brew pub on 4th Street just a few minutes south of the Stadium. I would recommend a stop there when you are heading up to or back from the game.