Well, that's a lot of ground to cover and you'll probably have to prioritize some things as you would otherwise have to bounce around too much. The Gettysburg, Valley Forge etc. have already been mentioned. In Northern Virginia you have some of the other Civil War battlegrounds. In the Shenandoah Valley at Leesburg there is VMI and Washington & Lee (all together side by side, plus the final resting spot of R.E. Lee. Richmond has the Museum of the Confederacy with original revolvers and swords of some of the Generals plus the Southern "White House"- right off the Highway about a 3-4 minute drive and takes about an hour to see. In the Philly area besides Valley Forge you might want to see the Liberty Bell and Independence Hall, the Declaration of Independence, etc. In New York, there is some interesting Dutch architecture along the Hudson River (Kingston) and if you go that route you would want to see West Point. There is also a small firearms Museum at West Point. Farther up is Ft. Ticonderoga at Lake George area. There is the Saratoga Battlefield as well. VT and NH- as far as museums, etc. I'm not sure there is that much but the scenery is nice. Connecticut. In Hartford is the State Library. It is the State Library that has the Colt Firearms Collection- I think the most extensive, all the old percussion revolvers, revolving rifles and carbines, etc. Mystic Seaport in Connecticut is good if you like whaling. In New London is the U.S. Coast Guard Academy and the U.S. Eagle training ship. Newport Rhode Island has all the mansions- probably worth a look (I guess). In Massachusetts there is the mentioned Lexington Green and Concord Battlefield (now a park) plus in downtown Boston the Old North Church and the U.S. Constitution. The U.S. Constitution (Old Ironsides) is well worth a look. At Newburyport is a small museum of the China Trade back in the 1840's. In Maine- not many museums I know about, just grab a lobster Dinner.
Worchester Mass has a museum with medieval armor if you like Knights in shining armor. This closed last year, did't it -- drawing a blank on name!? I should mention, the northeast is a crowded area with lots of houses and roads and people so a lot of what you'll want to see near cities- it will be in crowded surrounding. If you ever went over to Houston to see the San Jacinto Battlefield- surrounded by highways, oil and gas tanks, etc.- some of the Northeast stuff will be similar.
Planning a big trip- that's half the fun. Good luck.
The central part of New York State (Utica- Syracuse) not many museums. Pennsylvania is sort of the same (Wilkes Bare area).
Maybe go up through eastern VA and hit Richmond, Washington, the Civil War Battlefields, then from Wash to go Gettysburg- (or maybe on the way back) then Philly and Connecticut up to Boston and along the shore to ME then across VT and NH to Ft. Ticonderoga and down the Hudson to West Point and then west back to VA or all the way thru PA to OH.
Lots of options.