That's going to be rough. You've picked a "Gold Coast" area where anything waterfront is terribly expensive and very territorial. Many areas will not allow liveaboards due to local politics. It is possible to live aboard on the sly (unofficially and illegally but with marinas turning their back) but anyplace that does allow it? Will be top dollar and typically with a long waiting list.
There's the 79th Street Boat Basin on the west side of Manhattan, probably a ten-year waiting list assuming you buy a hulk that is already in the mud there. Some of the NJ side marinas (Port Liberte & Newport?) across from Manhattan may allow liveaboards, but they have little shelter and you will roll all the time. On the North Shore of Long Island...I don't know of any legally. Possibly Capri in Port Washington, they would know if there are any around. The shore of CT and points north is out of my local knowledge, you might try looking in Soundings, a publication that is local to the area. I know Boston has/had liveaboard space but again, it will cost dearly.
It isn't impossible--but it won't be easy. And with waterfront being so dear, there is no guarantee that anything you find will remain available from year to year.