Since you're heading to the eastern end of Long Island, an option to consider would be to bypass The City altogether.
H E R E is a link to the Bridgeport & Port Jefferson Steamship Company; take the ferry across Long Island Sound from Bridgeport CT, and you won't have to worry about bridge(s) tolls, expressway tolls, heavy traffic, etc in NYC and Nassau County. Trailers can be accommodated; while it's not cheap, relatively speaking, it's a lot less hassle than trying to get through NYC. And it adds an element of adventure to the trip, experiencing the ocean air as you relax crossing over to Long Island! If it were me, I sure would opt for this rather than trying to drive through The City at any time of day or night.