My folks live in Massillon (CAK area), the Mrs is from Vermillion (between Sandusky and CLE) so I knew a lot about the area.
There is Amish Country about 30 minutes south of CAK. Good food, good shopping, pretty scenery, if you are into that kind of thing. Remember, things will be closed on Sundays for the most part there.
I was just at Hocking Hills in June and it is very very pretty. We went camping with SIL and her family and would definitely go back.
CLE also has lots to do, Cedar Point is good too, as people have noted. If you're looking at CVG, don't forget about Kings Island.
Don't forget about the Football Hall of Fame in Canton, about 10 minutes south of CAK airport.