Taking a strong dog to New Jersey parks
Dogs are welcome in much of the park system, but areas such as beaches and buildings are commonly closed to them.

State park habits
A PetFriendlyTravel summary of the state park pet policy says pets must be on a leash no longer than six feet and under the handler's physical control, and that they are kept out of buildings and swimming beaches. That is a secondary summary; verify the posted rule where you plan to go.
Camping with a dog
The NJ State Park Service pet friendly camping page says select campgrounds welcome pets for an extra $5.00 per night. Book a pet-friendly site rather than assuming any site will do.

A federal neighbor
Delaware Water Gap National Recreation Area publishes its own Delaware Water Gap pet page. Federal sites set their own rules, so check it separately from the state rules.
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