Emma,
I haven't been to Lancaster County in a long time. Given everything else potentially on your plate, if you think you'll visit Ohio in a few years, perhaps wait until you can visit the larger and more rural Ohio Amish Country.
Here IMO are some of the top history attractions along your itinerary (assuming you're bagging Pittsburgh, NF and points further west). Note that the U.S. has excellent battlefield parks compared to many countries, with excellent visitors centers which generally feature a good film, artifacts, etc. Several of the parks have licensed guides, much as London, but relatively unusual in the U.S.
1) Boston Freedom Trail, especially IMO the U.S.S. Constitution, the oldest active warship in the world.
2) Saratoga, where one of the most consequential battles in world history was fought. Saratoga Springs also is an enjoyable historical resort, especially if you enjoy horse racing. This would be a detour from Boston to Philadelphia, but it is one of the most important historical locations in the U.S. Some very interesting characters also were involved in the battle, including British General Gentleman Johnny Burgoyne, a playboy general; frontiersman Daniel Morgan, a relatively unknown historical figure who perhaps was a key catalyst in the American victory in its Revolutionary War; hero-to-turn-traitor Benedict Arnold; and a devoted wife of a German mercenary officer, whose life in America would be worthy of a movie.
If you go to the Saratoga National Historical Park, be certain to see the Benedict Arnold boot memorial. Arnold, whose name is synonymous with "traitor" in the U.S. for his actions at West Point and afterwards, was nonetheless one of the heroes of the early years of the American Revolution, and a key figure in the American victory at Saratoga. The Saratoga Battle Monument has an empty facade that surely would have honored Arnold were it not for his subsequent treachery.
http://www.nps.gov/sara/index.htm
https://en.wikipedia.org/wiki/Battles_of_Saratoga
http://www.nps.gov/sara/historyculture/index.htm
Friederika Charlotte Riedesel, the wife of a general leading German mercenary forces, kept a journal of her adventures in North America, which includes the Saratoga campaign and its aftermath. As a result, she, along with Arnold and Daniel Morgan, are IMO the most interesting historic figures of the campaign.
http://en.wikipedia.org/wiki/Frederika_Charlotte_Riedesel
Here is her account of her travails in North America, although only pp. 167-190 directly cover the Battles of Saratoga.
http://en.wikipedia.org/wiki/Frederika_Charlotte_Riedesel
Morgan, who had earlier in his life survived a British whipping that could have killed him, developed revolutionary tactics at Saratoga employing frontiersmen sharpshooters armed with long rifles protected by conventional infantry. The American conventional infantry protected Morgan's riflemen from British infantry armed with conventional muskets which had a much higher rate of fire despite their much shorter range and lesser accuracy. Contrary to European custom, Morgan's riflemen targeted the British officers. This was perhaps the first instance in military history that rifles were employed as decisive military weapons. British officers understandably reported that they had never in their careers experienced such fierce fire.
Morgan later also engineered a decisive American victory in the southern theater at the Cowpens, introducing new tactics to employ militia, highlighted in the final battle sequence of Mel Gibson's "The Patriot."
http://www.his.jrshelby.com/kimocowp/morgan.htm
http://en.wikipedia.org/wiki/Daniel_Morgan
2) Hudson River Valley, including Hyde Park and West Point.
3) Gettysburg, site of the greatest battle ever fought in North America, and the most visited of all American Civil War battlefields. Nearby is Antietam, site of the bloodiest day in American history (Gettysburg was a 3-day battle) and Harpers Ferry Historical Park, which features historic vistas such as Jefferson's Rock. Here's an excellent trip report (click on the poster's avatar to check the poster's associated trip reports/reviews for Philadelphia and Washington, DC, which you should find very helpful):
http://www.tripadvisor.com/ShowTopic-g60798-i335-k3863513-Trip_Report_3_days_in_Gettysburg_with_teenagers-Gettysburg_Pennsylvania.html#28099317
http://www.gettysburgtourguides.org/battlefieldtours.html
If interested in Gettysburg, you'll want at least one night there. The Eisenhower National Historic Site also is located in Gettysburg.
4) Historic sites outside of Washington, DC. These include the Udvar-Hazy Center of the Smithsonian National Air & Space Museum, the greatest collection of aviation and space artifacts in the world; Charlottesville/Monticello; Appomattox; Williamsburg; Yorktown; Mount Vernon; Norfolk (tour the world's largest naval base and the U.S.S. Wisconsin; Baltimore (the B&O Railroad Museum, National Aquarium, Fort McHenry), and much more.
http://www.tripadvisor.com/ShowTopic-g1-i12567-k6510394-6_Days_from_Washington_DC_to_New_York_City-Road_Trips.html#49648937
You may want only two nights in Philadelphia, assuming one of those is a travel night from Boston. IMO, the historical attractions and non-art museums in Washington are much more numerous and superior.
Here are some websites that may be useful for your time in Washington, DC.
http://thedistrict.com/
Hopefully the following web page will be updated shortly for the 2013 season. Unfortunately, it may be greatly curtailed due to the U.S. budget sequester.
http://www.nps.gov/ncro/publicaffairs/summerinthecity.htm
If you fly into Boston and out of Washington, DC, consider taking Amtrak from Boston to Philadelphia, or even a bus (Megabus, Bolt or Greyhound) if you want to cut your budget. Then continue to Washington by train or bus and rent a car there for a road trip loop. You can include Gettysburg in this road trip. You'll save several days of car rentals and parking charges can be expensive in Boston, Philadelphia and Washington, DC. Car rentals often are cheaper from non-airport agencies, because you avoid airport taxes, but perhaps not if you use a foreign consolidator.
If interested in amusement parks, check out Philadelphia for the poster's favorite amusement park -- Six Flags Great Adventure -- along your route.
http://ridesandotherstuff.wordpress.com/
Boston and especially Washington especially have good nightlife. Check travel articles for both cities, use the search engine in the destination forums, or actually post to find what the entertainment options that most appeal to you.
You will find more than enough attractions to occupy two weeks in the northeast corridor.
Good planning!