Couple of things...
The only way to actually ride into Manhattan from that side is the G.W. Bridge, so if you are dead set on actually riding into the city, you will need to get yourself there. One resource you might check with for assistance in that neck of the woods is the Bicycle Touring Club of North Jersey.
If you go to Stroudburg, you can get yourself to nearby Delaware Water Gap, PA where you can pick up AC's Atlantic Coast route north to Middletown, NY east of Otisville. A combination of New York State bicycle routes Nos. 17 and 9 will get you from Middletown into NYC:https://www.nysdot.gov/divisions/operating/opdm/local-programs-bureau/repository/bicycle/regional-bicycle-routes/region8/signed-state-bicycle-routes.html
Our you could take the AC route south from the Gap to Lambertville, NJ. From there, there is a spur that takes you to somewhere in N. Jersey (Summitt, perhaps) where you catch a train into NYC.
If you decide you want to ride through Lambertville, I can give you a cue sheet for an amazing route to Hoboken, NJ, where you can take a nice ferry ride to the NYC path along the Hudson. The only catch is that the route is only safe on weekends because it goes stright up the heart of the Port of Elizabeth and Newark. You also have to be comfortable riding in some urban traffic. (Amazingly, most the vast majority of the 90 miles is rural to suburban.) And you doing it in one day fully loaded might be a chore. Our club does it every year on the Sunday before Labor Day. Send me a PM if you are interested.