Travel along the Garden State Parkway, and you'll see a number of outlets that look like exits but aren't. Usually, they're at the far ends of rest areas or on the side of the road adjoining a neighborhood, and they have big warning signs that promise huge fines, several thousand points on the transgressor's drivers license, and certain death. (Okay, I'm exaggerating about the points and kidding about the death part, though the insurance surcharge from the points would likely bring about a fatal heart attack.) They're generally there so that the State Police and emergency vehicles can easily move between the highway and local streets when the road is congested or otherwise difficult to access.
I know of one un-numbered exit that's totally legal. If you find it, you can drive right through it and onto local roads.
I promised I wouldn't divulge the exact location, but it's accessible from one of the southern rest areas. Ivan showed me once, when we were on a birding expedition. If memory serves, there's even a traffic light at the end of the access road. And there's no toll booth. That should give you a hint to its whereabouts, because if it was anyplace really popular, you can be sure the Highway Authority would be collecting its share of revenue from it.
Any idea where it is?