My favorites that others have said: Barcelona, G Michaels, Rigsby's, The Rossi
The Pearl, right next to Lemongrass.
Great small plates/appetizers, amazing seafoods (oysters, clams, shrimp) prepared a few different ways. I really love their raw oysters. They're fresh, they typically have at least 3 different types, though I've seen as many as 7.
If seafood's not your thing, but you want to do upscale, Lindeys is amazing. Without a doubt the best service experience I've ever had in Columbus. The food is original, amazing, and well portioned (not too much not too little). The servers are professionals and know what it is to provide a fine dining experience without looking down their nose at you.
Lastly, I'd suggest trying out The Table some time. It's another place my gf and I will go to order a smorgasbord of small plates and eat off each other's plates.
http://www.thetablecolumbus.com/#!menus/c1jo3
Definitely not one of the better known places, but it should be.