Buy copy of ELDRIDGE you will find the entire route well documented including a lot of tide and current information for planning the trip. If the wx is rough, you'll need to stay inshore but if the wx is good, by all means head out and enjoy the ride.
The warning about the Jersey shore should be taken seriously--I knew someone who was lost and presumed drowned within sight of the shore, the shoals run much further out than you would think and opposing wind and water can make for some nasty waves and slams on the shoals.
But given good wx, this can be a beautiful passage. Coming into NY harbor at night from the sea is a beautiful sight. Just beware the commercial traffic--some don't keep any watch, others can't manuever because of channel restrictions.