Hello. There are no legal places to wheel on LI or close to NYC. Unless you consider driving down a short, flat, muddy dirt road to be off-roading. I don’t. And the legality of some of these places even can’t be confirmed. So in my book, it’s not worth the time/effort/ potential risk to visit them.
There are private properties within a reasonable driving distance from LI/NYC that are excellent places to wheel, but you need to be in a club in order to gain access. Clubs form relationships with willing landowners and work out deals for access. Sometimes it’s labor/wheeling or $$small donation per rig to gain access.
Visit Northeast Offroad Vehicle Alliance or Northeast Association of 4WD clubs and take a look at their Member clubs for one that’s close to you and fits what you’re looking for.
Also, if you’re interested in learning how to drive Offroad safely and see what it’s all about, I recommend looking into taking a class at Northeast Offroad Adventures, or NYOffroaddriving.com
It’s a school located about 1.5hrs north of the city that offers professional instruction in everything from basic to advanced driving techniques, vehicle recovery, and all related topics concerning motorized outdoor recreation.
Good luck.