I’m travelling to New York and Washington DC for 3 weeks. What should I do and see?

I’m going over in October, Halloween – Yay – I’m 32, from Australia and have only ever seen 1 group of trick or treaters, but want to know the out of the way, must see, not included in guide books things to do, national parks to see and great bars and restaurants to go to that aren’t touristy. What are other states to visit in the area that would be worth a quick trip.
Also should I fly into DC and travel to NY or vice versa.
Thanks.
I know about things like Holocaust Museum, Smithsonian, Lincoln Memoral, look at the White House, Arlington. I found them in 30 seconds in google. it is the things you would never know about that I want to know about.

I’m travelling to New York and Washington DC for 3 weeks. What should I do and see?