While this is too late for this post, possibly someone reading this with a future trip might find it helpful....
If you are traveling to the Ohio area there are MANY great courses to sample including as Tar Heel pointed out the Ohio State Golf Course at OSU in Columbus. If you can get on it, Double Eagle is a great track in north Columbus as well as The Golf Club... Scioto is very popular being the course Jack Nicklaus grew up on but again very private...if you belong to a club maybe your pro can make a call for you!
Enjoy!