Directionally this is a state of complete paradox. North Westward you have the bliss-ed out and low-self-esteem mess that is Toledo. But if you travel there from the south (Dayton) you see little towns like Findlay, Ada, And where I live, Bluffton. Dayton itself is pretty sprawled out, but there's a loot to do there and has been every time I've visited...which is fairly often, I have family there. BUT the surrounding area is confusing to navigate and empty of attraction. Cincinnati has art museums and parks, and of course the gigantic international market that is Jungle Jims. And yet, next to Cleveland seems to get the worst rap of any big(er) cities in Ohio.
I like Cuyahoga National Park. It took me a while to get my bearings, which might or might not mean it's laid out weird. I haven't actually been to Columbus. But it has the 'Short North' that is the drive from University to downtown. Also it has German Village and COSI. So it's probably worth checking out. As I said, I live in Bluffton Ohio, it's about an hour South of Toledo and has a Mennonite University that brings its population up to near 5,000 people. I love that about it; you can walk the whole town abreast in 20 minutes!