I think that you will find some good hunting here. Enjoy your stay and good luck!
There are no permits required but you will have some of the same restrictions you have on the mainland. A lot of the historical sites in San Juan are National Parks. Public beaches are permitted but there are a couple of state run beaches that have objected to my hunting them. There is no rule against it but I was not looking to make enemies either.
There are some beaches, especially along the South coast that have a thin layer of yellow sand upon a gray, muddy bottom. I began hunting at a beach like this and it turned the beautiful yellow bottom to a dark gray mess.
I immediately stopped, even though the area was rich in finds. Because there was little current or wave action, it was clear that it would take a long time for the area to recover. As a beach hunter, I will not be mar a pristine area for personal gain or enjoyment. I hope you would agree with this principle as well.
Most of the beaches on the North, East and West coasts do not have as delicate an ecosystem and recover quickly with the help of currents and wave action.
The only other important advice I can offer is to bring some vinegar along in case you run into any jellies. Scrape any jellyfish burn with a credit card or something similar to remove the microscopic barbs. Do not rub the area! Wash the area with generous amounts of vinegar.
Do not forget your sunscreen, polarized sunglasses and water shoes. The water is full of broken glass and jagged cans.