[Robocat1]

Ohio's not a big state, so you can do all of this with a max. of three hours drive between each:

-Youngstown (near PA border, on Rt. 80) - Steel Museum, Children's Museum, Mill Creek Park - Old Mill
-Go west on Rt. 80 & north to Cleveland - Great Lakes Science Center (team party for Buckeye Regional this year - soooo much fun stuff to do!) and, of course, The Rock&Roll Hall of Fame (next door to each other)
-West to Sandusky - Cedar Point (best rollercoasters in the world, I think), or South/East to Aurora, Geagua Lake (more rollercoasters). Both sponsor Physics Days so I'm pretty sure if you call ahead you can get a park employee to give you a behind the scenes overview. The have FIRST teams display there every year to display on Physics day (coordinated by Cleveland NASA). And there's another hugh amusement park in Cincinnatti but I forget the name because Geagua Lake and Cedar Point are sooo awesome that I haven't gone there in at least 15 years!
-South to Columbus (COSI, state capital, the Horseshoe at OSU, etc.)
Of course, lots of really big malls and shopping everywhere!

And, there's much more (boating, train rides, water parks, camping, Amish areas, River Boats - go a little further south to the souther boarder - etc.)

And don't forget baseball, football, soccer, hockey...