If you have any OSU connections, the Scarlet is worth trying to get on. The Nicklaus re-do has drawn mixed reviews but I still think it is worth the effort and, at least in the past, access was not that difficult.
I am a big fan of Granville (although Brent Hutto is much kinder to the four "new" holes than I am). The 14 Ross holes still in existence are very good, with small greens and subtle challenges. It is probably an hour from the campus area.
Champions is also very good. The formerly private Winding Hollow Country Club is a Robert Trent Jones, Sr. design with small greens, a fairly intimate routing and some neat elevation changes. Champions is inside the 270 outerbelt and is a 20 minute drive from the campus area.
Another good option is Tartan East. Although it is an Art Hills design, it is pretty well done. This is, again, the formerly private Winding Hollow Country Club. The club moved to this site when the area around the Champions venue deteriorated economically. Unfortunately, the financials did not work out at this location and it went belly up. However, it has been reincarnated as Tartan East and provides a pretty challenging round on a fairly flat, heavily wooded piece of property. More modern design elements are present here than at Granville or Champions but it is a decent option. Probably 30-40 minutes from campus.
The other options discussed here are fine also. Cook's Creek is a favorite of mine. The Golf Club of Dublin has grown on me over time but, unless they are running a special, is a bit overpriced. Longaberger is a mixed bag: a great site with some very average golf holes. It is no longer that hard to get on but I feel no real hurry to get back there and the other options presented in this thread are much less expensive.
Enjoy the weekend in Columbus.