I am about 35 miles north of Cincinnati just east of Lebanon. I drive the hour to Dayton motor sports because the vic dealer in sharonville is a total ass. As far as roads I like light traffic with curves and hills. I don't like downtown city traffic.
Well, you're in a nice area just east of Lebanon. I'm just up the street from you.
Plenty of nice, hilly, and occasionally twisty roads around the Caesar's Creek area.
If you're up for longer day trips, you can beat along the river east over to Portsmouth. There are plenty of backroads you can divert yourself on without worry if you have a GPS. Be advised that many in the country end up gravel if that kinda thing concerns you.
If you head south, you can cross over into Ky, where there is a lot of hilly/curvy riding. One of my favorite is Ky 22. You can watch a nutbag traverse it in a pickup in the thread "Why I shouldn't apply for a concealed carry permit." The one thing about Ky roads is there is a lot of blind hill cresting. Be aware that the roads aren't always straight on the other side of the crest. Eastern Ky is nice too, though it is a bit far for a day ride.
If you head northeast, you can explore the Hocking Hills area and get home in a day. Some very nice roads and various parks and caves to explore.
If you can spend a night, I would highly recommend the area around Marietta or the backroads between Newark and Massillon. These are by far the prettiest areas of Ohio IMO and the roads are really fun and mostly free of traffic; though the Quaker stores between Newark and Massillon can draw good crowds in the summer on the weekends.
If you have a little extra time, I HIGHLY recommend West Virginia. That is probably the best state in the US for motorcyclists who enjoy technical riding.
Some people make a lot of Southern Indiana. Personally, I've found very few twisty roads there, and they were mostly littered with gravel. There are a lot of straight roads that run up and down hills if you like the roller coaster stomach drop sensation.
There is another guy who posts here regularly by the handle of Lazy Dawg who lives nearby. Maybe next summer we can all meet up somewhere for lunch and take a little country ride?
Good time to dream and scheme while it's too crappy to do much outside.