Are dogs allowed anywhere in seaside heights? Beaches? Boardwalk? What if it’s in its carrier?
generally no, there may be early morning (before 9 am) ability for you to walk on the boards with your dog. But the reality is, too many irresponsible dog owners don't clean up and claim their dogs are friendly and you only need one bite for a big problem to ensue. You should call the police dept to confirm what you can and can't do. You can bring your dog (on a lead) to island beach state park at the south end of the barrier island.
Seaside Heights is a long, slim stretch of land between two bodies of water - the ocean (the big one) and the bay (smaller) There's a nice sidewalk along the bay which you can reach by bearing right as you come onto the island over the causeway, then, instead of going to the left to the ocean, go two blocks over as soon as possible to the right. You can park along there and walk the pups.