The only way you can actually ride into NYC from NJ is via the George Washington Bridge way up north.
There are several rail and ferry options to Manhattan, but there are bike restrictions on the rail options during weekdays and certain holidays. Every year my local club does a ride from New Hope, PA (which is on ACA's Atlantic Coast route) to Brooklyn. We cross into Lambertville, NJ (also on the ACA route) and then take a mostly different route to Hoboken, NJ, where we catch the ferry to Manhattan and then ride over the Brooklyn Bridge. The ferry ride is very nice. It lets you off on/near the MUP that runs along the Hudson River.
I think our route and the ACA spur to NYC have a few common points, including Summit, NJ, where the spur ends and you take the train. When the time comes, I can give you the route from there to Hoboken with the proviso that it can only be ridden on the weekends, and preferably Sunday. That's because it goes through the Port of Elizabeth & Newark. Riding through there on a weekday would mean suicide by truck.
Our route does pass through Jersey City in North Jersey, a town with a less than stellar reputation. However, it avoids the really bad sections of that town. In the 16 years we have been riding to Brooklyn, no one has ever been the victim of violence. In fact, we often get cheers from the locals. But if riding through areas with poor people who don't look like you is frightening, I recommend that you stop in Summit and take the train to Penn Station.