Hi S. Welcome. I'm in NJ, and have been diving local waters for more than 50 years, mostly the inlets. Before you do any spear fishing check the fish and wildlife commission regulations. Even though no NJ license is required for salt water fishing, there is a Federal permit that you can get on the NJ Fish and Wildlife web site. There are many regulations covering spear fishing, and in fresh water the state regs forbid the taking of ANY game fish. Check those regulations carefully, both fresh and saltwater.
NJ has very little structure in open ocean waters shallow enough to free dive. Mostly just sand, with very very fast moving fish. Jetties, inlets and rivers are where you will find the best opportunities for spear fishing. All of the regs that apply to rod and reel angling apply to spear fishing, and then some additional. NJ diving is challenging, but can be very rewarding. The only fishing I do these days is with a hand net, collecting tropical Gulf Stream strays. These brilliant little fishes can be extremely numerous in late summer. Dropping water temps kill them all in October.
There are at least two websites that cover NJ diving. Lots of good information. There are so many rod and reel fisherman it can be difficult to avoid disturbing them, and they become hostile very easily when someone is diving where they are fishing. The amount of broken off monofilament line in the water can be dangerous. I always carry three separate and different line cutting tools. Good luck and be cautious.