I was toying with the idea of visiting the US either next year or 2026, and not only is the northeast the cheapest destination to fly to, but to my limited knowledge offers the most things to see. (unless you can persuade me in favor of, idk, the midwest, the south, whatever)
What I was thinking of visiting:
The Empire's HQ (D.C.) - obvious choice. Imperial architecture, containing probably one of the most famous museum complexes in the world.
Annapolis, Maryland - looks like a quaint seaside town (or maybe Baltimore, MD, with its antique ships in the harbor. Though I hear it's a bit rough)
Harper's Ferry, West Virginia - John Brown! Plus, it's in West Virginia - an excuse to cross one more border.
Philadelphia and Boston have old colonizer architecture and legacy stuff... but to my understanding, basically nothing is left. No idea if there's anything on indigenous culture in that part of the country.
New York City - One of the cities, for good or ill.
I'm definitely also going to New Haven, CT. I have no idea what's there, but I have something to prove to a comrade (or get owned) 
Also I'll probably have around a week, and I should have my license by then, so was thinking of renting a car. Seemingly, the car brain is strong enough that rental fees are surprisingly low.
You can't do all of those in a week; at least, not in any kind of meaningful way.
Boston and NYC are kind of cool. D.C. is definitely a city, but has some cool museums.
Try the crabcakes if you find yourself in Maryland.
Everywhere has good food though.
You can use Amtrak to get between Boston and DC, (Including New Haven, and NYC). D.C has a metro, NYC has an expansive subway. New Haven (and CT in general) have only just started focusing on public transportation.
What do you want to prove in New Haven?
If you want something totally different, the Fall foliage is always really pretty in New England, and October is the best time to see it.