Well, I only know of a couple of alternatives a bit south of you. There's Target World on Kemper Rd. in the Tri-Couty Mall area north of Cincinnati. It's kind of expensive, as ranges go, but you can rent guns there and set the target distance with movable hangers. There is also supposedly a new mom & pop range that's an extension of the gun shop in New Miami (just outside Hamilton). I don't know the name of the place and it's only been up a few months, but I can look into it. The only other alternatives I know of are private clubs or knowing someone with private land outside the city limits.
As for me, I'm on probation and can't handle guns outside of work for probably a couple of months yet. I'd be glad to go on a range trip then though.