My wife and I took our 4 wee ones (2, 4, 8, 9) camping for a few nights in Pennsylvania at a place called Knoebels.
http://www.knoebels.com/
I cant begin to tell you what a great time we had. This is an old time amusement park with classic and new rides with a campground.
I have never tasted any better food at any park better then at this place. My wife and I would giggle every time we paid for anything because of the value. We live near the Boardwalks in NJ and everything there is so expensive, so paying $20 for all of us to eat Breakfast and have food left over is a pleasant surprise. The one thing that was really disappointing about our stay was that I didnt have a chance to try all their food.
The admission into the park is FREE, FREE parking and FREE entertainment. It seems that a lot of the campers would watch the evening show at the park then head back to the camp fires.
The camping at their campground is tight and no privacy. You are right on top of your neighbors, but the ease of walking right to the park is way worth it with 4 wee ones. They even have spots along side of one of their wooden rollercoasters.
We did cruise around the area and found a few coved bridges and and a quieter campground with a lot more room down the road. (J & D Campground) There was even a cute little ice cream shop across the street, but we didnt stay there. We might this year thou.
This place is defiantly a hidden gem and we will be making it a yearly visit. For such an unknown place, it has won many awards, even beating out the mouse.
(Golden Ticket Awards)
http://www.knoebels.com/pdfs/GoldTix07.pdf
As for central New Jersey, Turkey Swamp is the only place I would and have camped at.
http://www.monmouthcountyparks.com/page.asp?agency=130&Id=2540