Although greater metropolitan Lima is in Ohio's flat, rectangular cornpatch, Ohio has some terrific riding roads. I'm sure some of my fellow statesmen will be telling you about them. But until you hear more, consider almost any Ohio highway with three digits to be a good candidate - and in particular, check out OH 555 and OH 550 - both in southeastern Ohio. Look closely at a side trip over to Hocking county, where the roads are all crooked, and all the hills are good looking.
The section of Amish country around Millersburg is gorgeous. Remember to take the back roads (Shaw's Law number 16: "All roads go somewhere - usually"). Don't be afraid of getting lost - it's more fun if you do. Do be careful of the horse drawn buggies and carts, though. With you doing the speed limit (oh, sure!) and them clipping along at 5 mph, they come up fast. And, while not as slick as goose crap, horse manure lacks traction [zing, thunk, ouch]
A terrific day's ride is OH 93 south to OH 555 south to the Ohio River to 7 (to Marietta) to OH 26 north to OH 800 north. Get off at 250, and visit nearby Mathias BMW (my favorite dealer in four states). Tell owner Gene Robinson and techs Dave and Jamie I said hello - and to offer you the free synthetic air they give to all who mention my name.