Mohican State Park is a great place to spend a day hiking and enjoying the outdoors.
There is a great covered bridge that you can go through, if you don't get to see many of those.
You can climb a fire lookout tower and overlook the forrest and hills.
It is very near to Amish shopping. Your wife may enjoy that.
You will definitely enjoy the Amish foods (cheeses, summer sausage, candy, etc...)
There is plenty of nice places to stay around there, as well.
If you guys like that sort of thing, there is a pretty cool Indian mound, called serpent mound, in south-western ohio. It is worth a look if you are within an hour of it. (It is good history for the kids, but not all that exciting, and definitely not an all-day destination).
The Rock and Roll hall of fame in Cleveland is pretty fun. There is a WWII sub very close-by (1 block) that you can tour (inside).
There is a great childrens' museum in Columbus, called COSI, which is a multi-state destination that has great exhibits and is very interactive. It is a great place for kids like yours (agewise).
Cincy has a great aquarium (Newport) that is just over the river (in KY). They aso have a world renowned BBW rib place (Montgomery Inn).
ETA: Dearborn/Henry Ford Museum is a wonderful suggestion. It is actually two parts... enormous indoor museum of all things Americana from all eras (from jewelry, to sewing machines, to tractors, to steam engines), and the other half is a real outdoor village of historical buildings, like the Wright Bro's house aand workshop, and Thomas Edison's workshop, etc... It is a great learning experience for children. You will not run out of things to do for 2 days.
ETA II: How could I forget the Dayton United States Air Force Museum!? This is the most amazing museum in the several state region. It is enormous, and is THE USAF museum. It has some incredible historic airplanes. To give a perspective of size, it has a B52 and SR-71 and B29-(I think?)
all under-roof, along with about 150 other aircraft under the same roof.