I’m a mom in Ohio – OHmomIO, get it? Anyway…
I’m about an hour away from Holmes County/Amish Country, and there’s lots to do there that’s hands on and sort of living history (although, it’s mostly shopping, but you get to see how they make stuff like furniture, cheese, etc.). Our kids love Amish Country, especially Lehman’s Hardware store (for the old fashioned toys) and the Smucker’s Factory/Store/Museum (we call it the peanut butter and jelly museum). In Dover, check out the Warther Museum of train carvings, and in Chilicothe go to Roscoe Village. Mansfield has the old prison, and the Living Bible Museum.
In Canton, Ohio, there’s everything President McKinley (momument, museum, First Ladies’ Library, etc.), the Pro Football Hall of Fame, and London’s Chocolate Factory (I think you have to call ahead for a tour).
In Akron (this is me), there’s a small zoo, but it has a lot of neat things and doesn’t take too long to go through – you could do it in a morning. Stan Hywet Hall and Gardens is the mansion built by the founder of Goodyear Rubber, and it’s a good tour. And another living history site would be Hale Farm and Village. Akron has a lot of Underground Railroad sites – Perkins Mansion, John Brown House, the historic church in Tallmadge Circle. You could also see Derby Downs where they host the All-American Soap Box Derby, but other than drive by it, unless there’s a race going on, you can’t really tour it. You could even go watch the Goodyear Blimp take off from it’s hangar in Suffield, Ohio – that would be waaaay off the beaten path, but it has the Wingfoot Lake State Park right across the lake from the hangar and there’s stuff to do there, too.
If you come in March, which I know you’re not, there’s a ton of maple sugaring events in NE Ohio, and I think the biggest one is in Burton, Ohio.
If you’re in the Cincinnati/Dayton area, you could go to the Air Force Museum at Wright-Patt, and it’s FREE admission. We went when our son was four, and he got into it. It’s very stroller-friendly. And, it’s in Kentucky, but the Newport Aquarium is good (we plan on going when we’re in Cincinnati for the homeschool convention). And there’s tons to do in Columbus.
Toledo has the zoo and state park and such, but for a real adventure, take the ferry over to Kelley’s Island State Park, and then you’ll have a whole island to explore, and right across from the state park are the “glacial grooves” which is a giant rock that was (supposedly) cut by glaciers, but of course, you can teach your kids the Flood explanation, which is what we do. Might be a nice visit after the Creation Museum while the Biblical facts are very fresh and reinforced. Sandusky has Cedar Point, of course, but next door in Port Clinton there’s a drive-through wildlife park, and Marblehead has the famous lighthouse.
If I think of any more I’ll add on, but you’re sure to be busy in Ohio with very wholesome family activities and lots of history and nature. There are at least eight presidential homes, birthplaces, or memorials you can visit, too.