I do not live in the east coast.
But here is what I found in a quick search.
It seems New York state really does not appreciate 4X4 recreation. This is all I could find from their public park website
Even worse, it seems New Jersey has NO legal off-road parks at all
. With all that, your best bet would be National Forest Service roads, and Bureau of Land Management trails.
U.S. Forest Service locations in New York state
There are no National Forests in the State of New Jersey.
Off Highway Vehicle recreation is not available in eastern states within Bureau of Land Management areas
But after researching all that, any public access to dirt roads, trails, and OHV (off highway vehicle)/4X4 recreation areas is extremely limited in the states of New York and New Jersey. You will likely have to consider moving if you wish to find public access to dirt roads and public, legal off-road parks.