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.
There's plenty of places to visit in the US northeast/mid-atlantic, but all those locations is a lot of ground to cover. You'll be driving for hours upon hours, and it might eat pretty hard into your sight-seeing time if you're only spending a week. For example, New Haven to DC would be a 7 hour drive! And that's in pretty nasty/aggressive traffic. If you're just getting your license, you do not want to be driving in NYC (or Boston).
For example, you could spend a week in D.C. alone: it would take days to experience the Smithsonian fully, and then you have all the other landmarks and museums and other attractions. Alternatively, New York City and Connecticut/New Haven would also fill a week.
The other thing to note is that if you're vacationing in the northeast, you may be able to avoid renting a car if you'd prefer. This is the only region of the country with decent inter-city train travel (Amtrak), and D.C. and NYC have well-developed subway metros.
So for example DC + Maryland and NoVA?
I think that would work for the most part.