Seaside is not the nicest place in NJ.
I would suggest you look further south around Wildwood if you want a good boardwalk and great beach for the kids and close to Cape May for a great place to visit for the adults.
A campground between each that I have used is Beachcomer.
Welcome to Beachcomber Camping Resort
There are several other campgrounds in that area where as the selection is limited around Toms River.
While coming north this is a bit out of the way to cross southern Jersey but I think worth it.
You do want to make a reservation in the summer.