When people ask me about Ohio, I always whole-hartedly recommend Cincinnati.
But then you added "stuff to do within a reasonable driving distance," and I think that tips the scales in favor of Cleveland.
And if you want to leave the car at home, you can take Amtrak from Cleveland to New York, Chicago, Toronto, Philadelphia, Baltimore, and D.C.
I still love Cincinnati, but until international flying gets back in order, it's not an ideal starting point for adventure.