On long island there are very few legal places to wheel. If you see a trail head, there is a good chance that it is private property.
Some places that are legal on the island are..

Hither Hills park..Around montauk area. There are hunting trails, nothing difficult, depending on how much it rained..Just watch out during hunting season. No permit necessary, from what I've seen.

NY State 4 wheel drive Fishing permit. $49, you can drive on the beach for the purpose of fishing, at Gilgo, Robert moses, Sore thumb, Democrat point, Nappegue, Montauk Pt..

Smith Point Beach has a seperate permit.. a lot of money.. and it is a wheeling permit on the beach. They had a decent amount of beach and trails, all very easy BUT, due to errosion they might not be issuing them this year. And if they do it will be limited in access.. I think you also need a Green Key pass in order to buy the smith point permit..

If you want to get off the island to do some real wheeling..there is..
Paragon Adventure Park in Hazleton, Pa. about 3 1/2 hours away roughly, depending on where you are on the island..

Also..Rausch Creek..Tremont,Pa.. About 3 hours away depending..

Both are Pay to play offroading parks. normally about $35 per truck per day, and $5 per passenger per day. And you need to watch a video for both, and they require a three truck minimum per group..

If you havent signed up for it already, I highly recommend it..
ECXC.com East Coast Xterra Challenge July 22,23,24 weekend..A Yearly event that pulls in a ton of Xterras from all over the US. A great place to get introduced into wheeling..

Enjoy..