If I ain't too late to the party, here's a few suggestions for the Ohio leg:
The Columbus Zoo just opened a waterpark called Zoombezi Bay. It's hell of new so you probably won't get sick from the water. Also the zoo itself is pretty good.
If you like animals but are trying not to overdo traditional zoos, I suggest a visit to
The Wilds off I-70 near Zanesville, Ohio. It's more of a conservation center than zoo and you can take a safari-style trip through it rather than stroll from one glassed-off pen to another.
If you're going up I-77 towards Canton and Cleveland, you can make a stop at
Warther Carvings, a museum of this old-time crazy guy's intricate carvings of trains and other stuff. They also have a knife factory on-site that makes some pretty good stuff. It's relatively quiet - not a ton of whistles or chugga-chugga, considering it's pretty much all about trains. Easy to reach from the Dover/New Philly exits. I suggest it to people all the time as an alternative to the Pro Football Hall of Fame a little farther north in Canton.
Akron is home to the Inventor's Hall of Fame, which includes a hands-on "workshop" where kids can break, build and otherwise play around with stuff in the name of inspiring creativity. Also in Akron: Swenson's. Drive up, order some cheeseburgs, and enjoy them in the comfort of your car. If you want to visit some cool architecture, Stan Hywet Hall is the former home of the Goodyear tire family. It's a gorgeous tudor-style mansion with huge gardens in several different styles.
If you're going to be closer to Cincy or Dayton on your way up and don't mind stopping at a store as a tourist attraction,
Jungle Jim's International Market is like an amusement park of food and drink. It's absolutely insane, some of the stuff they sell.
I'm sure I can think of more stuff in Ohio if you're interested. My favorite Kentucky diversions are the Corvette museum in Bowling Green and the various distilleries along the Bourbon Trail.
Memphis is probably out of the way but Graceland is cool.
Isn't there a Mr. Rogers museum or park somewhere near Pittsburgh?