From your existing list, I take it you are most interested in nature places rather than sites of interest of the manmade variety? Most of the big national parks are in the west, but the east coast has beautiful areas as well. I would suggest:
Hiking part of the Appalachian Trail.
Fingerlakes (New York) are beautiful, and I hear Arcadia (Maine) is as well, though I've never been there.
The Greenbriar/New River Gorge in WVa is gorgeous.
Shenandoah Valley in VA is a nice national park.
Hershey Park is worth a visit, though that's a bit different than the other parks you've listed.
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Much of Central Pennsylvania Appalachia is stunning and filled with State Parks that are worth going to, but I can't remember any names off the top of my head.
Mammoth Cave in Kentucky would be an absolute must see if you can make it down there. Definitely the most amazing natural site in the east coast.
Well, there are some ideas for you. Most of the parks in the east are just forests and hills. Beautiful yes, but not striking in the way many of the western parks are. Speaking of western parks - one think you don't have listed is the Big Sur coast. If you've got time, rent a car and take a drive down Highway 1 from San Francisco going towards LA. Once you get past Carmel it's some of the most beautiful driving you'll ever do. It's worth the 2 hour or so drive and the cost of 1 day rental car.
EDIT: Oh, how could I forget! You should visit some of the Civil War battlefields. Especially Gettysburg! It's definitely worth a day trip. They've done a great job preserving the town and battlefield, and have an excellent visitor center. You can practically relive the entire battle. Antietam (in MD) is nice as well. Also, I've never been to Saratoga in NY but I've heard it's really been preserved well, too - though that's a different war.
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"What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?" - Richard P. Feynman