Uber/taxi/public for two days and save the headache and cost of driving in the city as a newbie. You’d spend about as much time in traffic in the city as you would driving to Palmyra.

In the event that you don’t fly into Buffalo, I’m not sure I’d prioritize Niagara Falls in your itinerary. Palmyra is certainly worth a half-day drive from NYC, and I’d plan at least part of a second day there so you can get the home, grove, hill and printer, as well as leaving time to go through Fayette on your way out.

But the time we went up there for a few days and stayed near Palmyra, I recall it being most of a day to get back and forth to the Canadian side of Niagara (the more scenic one) and do the boat and everything. It was a memory, but not equal to using up a full day for.

I’d go NYC for 2-3 days

6hr drive to Palmyra for the afternoon+next morning, leaving via Fayette on your way towards/near Philly, which is also about a half day drive.

Most of the significant Philly stuff is within a few blocks downtown, so you might supplement with something nearby like Valley Forge.

If you’ve got a little breathing room between Philly and Gettysburg, then consider routing through the Lancaster area with the Amish/Mennonite folks. I really thought it was neat to see the Hans Herr house which was built over 300 years ago — far older than anything else we saw on the east coast. You could stop at a dairy for some good ice cream, and get stuck behind a horse and buggy for 10 mins. Probably not worth a day, but worth a detour.

When we did Gettysburg, we stayed at a hotel right in town, which was nice. It’s an extensive enough battlefield that it takes at least a few hours to drive a few dozen stops, and you feel compelled to get out and walk around at several of them, especially Little Round Top and the cemetery where Lincoln gave his address. There’s also a museum there that you’ll want to leave time for.

Baltimore should at least be a possibility on your route with Ft McHenry, the Inner Harbor and Nat’l Aquarium, and Camden Yards (O’s tix often have lower demand). You’re close enough to DC at this point that if you stay the night here, you can still be at the Smithsonians when they open.

There’s enough in DC to fill 3-4 days, especially with the fireworks in there. With enough notice, by coordinating with your congressperson you can probably arrange a tour of the Capitol. Don’t miss the museum at Dulles even though it’s out of town. Your schedule might also allow enough time to make a loop through Monticello (way cooler than Mt Vernon if you could only see one founding father plantation) and Fredericksburg, both a few hours into Virginia.

Here would be my family’s 12 day itinerary:
1-3 Fly to NYC, see shows, baseball, museums
4 drive to Palmyra, see part
5 finish Palmyra get to Philly via Fayette
6 Philly and Valley Forge
7 2hr Lancaster detour half day Gettysburg
8 finish Gettysburg, get to B-more for baseball and Ft McHenry
9 DC Nat’l Mall and monuments, archives
10 DC Dulles Airport museum and Arlington
11 Monticello, Spy museum, baseball
12 Holocaust, more Smithsonian, fireworks