I would suggest spending about 45 mins browsing through this forum because a lot of people have already answered that question and they give other useful advice. but I'm moving to Columbus as well for grad school and I've heard that Grandview, Clintonview, and Victorian Village are nice areas relatively close to campus, but far enough away where there aren't that many undergrads.
My roommate and I found a nice two-bedroom apartment in Victorian Village. We're moving in June CAN'T WAIT