We did the trip from Cape May to Montauk last July. We stayed along the NJ coast and then the south shore of Long Island. We made the jump across the NY Harbor area at about 2:00 AM. There was very little shipping then.
The boat was very new to us and the winds were from the West, not sure I'd do the same if the winds were offshore.
At 6 foot draft (for us), the NJ coast has very few options if there are any waves at all. There are threads on Sailnet that relate this better. A quick search may turn some up.
Fun fact #2484: In my avatar, that's DavidPM at the helm of my boat.
Bland, non-political statement goes here.