They used to sell out of state day passes for the beach access for East Hamton area beaches. There is no more "dune" wheeling as the dunes have been protected for years due to beach erosion... There is also some old army structures that were built to look like homes from the ocean and have a bunch of trails off of them. A few fresh water fishing holes with some light 4 wheelling to get to them. Most only known by locals so you should go ask around in the town on how to get there. I have not lived in NY for 8 years so access may no longer be available to some of the areas...
Below is a link with some of the off road permit info....
http://mikepoz.com/off.html