It really depends on what interests you have.
If you're looking an awesome place for kids, the Great Wolf Lodge in Sandusky is a great indoor water park. Since Lake Erie is around 50F, this place comes handy this time of the year. : )
If you love beer, NE Ohio has many awesome microbreweries to visit. Thirsty Dog and Hoppin' Frog are located in Akron. Great Lakes Brewing is located near downtown Cleveland.
If you love hiking, Hocking Hills is the place to go. It's in the SE region of Ohio.
If you are into sports, I'd recommend you come to a Browns game. For a change, we are competitive this year. It's a fun experience
If you love fishing, look no further than Lake Erie. : )
I only fish now and then, so I couldn't tell you what bites this time of year.