I''d head outside of Long Island. Once you get below Sandy Hook, look into places to stop over in New Jersey.
I sailed up from Florida on the outside, and in the section from Cape May to New York, I sailed between the North/South shipping lanes in the traffic seperation buffer, which kept me free from any major traffic.
The ride down the Long Island Sound, through the bridges into the East River, then over to the Hudson, out the Verazanno, around Brooklyn and out to Sandy Hook will really take a lot out of you, and you''re not going to be doing as much sailing as you would outside, and, as others have mentioned, you''re really going to have to plan for the tides, not just going through Hells Gate, but also for going out through the Narrows (at the Veranzanno bridge). You don''t want to slog through 2 kts of current all the way to Sandy Hook