I'm not far from the OP. Here's a few ideas / experiences from our family trips over the last 20 years (some duplicates of other posts ideas).
Vermont - cooler summer weather, fair bit of outdoor activities including a day spent at the big granite quarry (supplier to many famous landmarks construction). Cool, quiet parks with ponds for swimming / canoeing / fishing. Lots of hiking / biking trials and other parks / landmarks to visit on day trips (or even a few hours out and back trip from the campsite).
Maine - Downeast area - camped near Ellsworth. Acadia Nat'l park, tons of local attractions like the loggers show. It was heckova drive overnight from MD, but worth it.
Put-In-Bay Ohio - very cool island in Lake Erie. Small island town you can get around easily on a bike or golf cart. Boating and fishing in the lake. History - Perry's Victory. Day trip to Cedar Point amusement park. Only thing I'm unsure of is how big of a camper you can get across the ferry to the island -- that could be a deal breaker for on the island, but we saw plenty of lakeside CG's on the mainland.
Smoky Mountains - Nantahala side around Sylva / Cherokee. As others have said, well worth the 14 hr drive. We spent about 4 days just exploring the interesting points of the park. Kids never had so much fun WITHOUT "commercial" entertainment. They got to see some big wildlife - some up close. Our only drawback was being in a commercial CG on a site too close to the road - one "local" was blatantly jealous of campers being "off" and yelled / beeped the horn / no muffler in his truck - made as much noise as he could each morning at 5:30 AM on his way past to work - by day 5 I was ready park my TV blocking the road and wait for his a@@!!
That area was important to me, as I lived there for a time as kid (Whittier, to be exact) and like being able to show my kids a little bit of my personal history. If heat is an issue (DW prefers cold / blizzards to summer heat) then don't go in August like we did - DW was miserable with the oppressive heat / humidity - at least as bad as that time of summer in MD, possibly worse. The kids also had a blast for day at the Zip-line place.
New River Gorge area of WV is also great, but we have never taken the kids along on that trip as they are now older and don't always vacation with us. We saw lots of summertime stuff advertised we would like to try a family vacation there, but we usually go for a winter getaway weekend when most of that is shut down for a nice quiet escape.
