Rbos,
There isn't any good way to get where you want to go. NYC drivers are all suicidal, but they have to be. Your best bet (short of chartering a barge in Cape May) would be to approach the city on I-78 and watch for I-287. Take I-287 south to Outer bridge crossing. Stay with I-287 that will take you to the Narrows Bridge (Verrazono?) (Narrows is where it is the Italian was the political name.) Across that, you are technically on Long Island.
You are on your own....
Matt - a refugee from Megapolios
Matt & Mary Colie
A sailor, his bride and their black dogs (one dear dog is waiting for us at the bridge) going to see some dry places that have Geocaches in a coach made the year we married.