Wisconsin- Oshkosh, without a doubt. But that's at the end of July/beginning of August. The Dells are a good tourist trap, though mainly for the kiddies, but there are some amazing sandstone cliffs with river tours available.
Take a day or two to see some of the Jersey shore, Cape May is an historic and beautiful area, and not TOO crowded early in the season (before the 4th.) Wildwood is more touristy, with a 3 mile long boardwalk that is more akin to a carnival's miday, and 5 miles of free public beach. Within a day's drive of NYC, DC, and many other urban areas.
I would recommend driving at least a portion of Skyline Drive in Virginia. Located in the Shenandoah National Park, it is a 105 mile long highway winding its way through the Blue Ridge mountains, overlooking the Shenandoah Valley, some of the most breathtaking views I've seen since my trip out west.
Rock and Roll Hall of Fame in Cleveland.
Musuem at Wright-Patterson AFB in Dayton, OH
. Every single aircraft in the Air Force's inventory is on display here, many you've never heard of. Including numerous examples of Air Force One (well, retired examples). You can walk through the plane that LBJ took the oath to office in after Kennady was shot.
These are off the top of my head... (I'm avoiding the obvious major metropolitan areas; NYC, DC, Chicago, Boston, ect. Any one of them could keep you busy for weeks of sight seeing)