There are no legal, public places to take your jeep that are close to you. The closest place, legal is in southern Jersey, the Pine Barrens. Check in the New Jersey regional section for more details like trail head locations, etc. In that section there are usually groups that go out quite regularly and I'm sure they'd be happy to have you tag along. Sometimes that's the best way to experience your first off roads trips, with a group.
There is also a great event coming up just a few hours north of you in Delaware County NY. Google "Tar Hollow 4WD Expedtion". This is a 3 day event held on pristine private property. Camping, wheeling, bon fires...trails range from easy not needing mods to "hero" sections where mods are needed. It is sponsored by OK4WD, a jeep store in NJ. and NJJA. Pre-registration is required through OK4WD's website. That's may 16, 17, 18.
There is also the Bantam Jeep Festival out in western PA on Father's day weekend. All kinds of jeep related activities great for the beginner with camping too....Check the post on here for that.
Otherwise, look into joining a club or hooking up with others from the NY regional forum. Clubs have access to private land that they workout deals for access with land owners.
There is also a group from the Hudson Valley area that meets up regularly. I've never joined them as of yet, but they seem like a nice bunch of jeepers and they're not too far away..
Good luck to you.