Have Clothes, Will Travel
It’s oddly difficult to find campsites in the Caribbean by Googling. Though not the most popular camping destination in the world, I did find with a lot of digging, a good number of proper campsites where you can pitch a tent.
The focus is on both dedicated and unofficial campsites where you can bring your own tent. Many of the same spots also have tents that you can rent.
I did this in Cuba, a country that does not have any official campsites. I set up my casita de campaña in all sorts of places at BnBs.
WWOOFING is a work trade website. You can find farms or ecovillages where you can volunteer your time in exchange for usually a free stay (lodging and usually food too).
There is a campsite on Sun Bay Vieques, a beautiful island off the south coast of the big island, in a National Park (Compañía De Parques Nacionales). The campsite has a cafe for food and drinks. Tent sites are in a flat, grassy, fenced area just off the beach.
The only campground on Culebra is right on Playa Flamenco. It is managed by the Department of Natural and Environmental Resources. This spot looks quite pristine and the beaches are really pretty.
El Yunque National Forest a USDA Forest Service park has dispersed and group camping sites. Camping is permitted at designated campsites only. Campfires are only permitted at Molindero and Old Nursery, in designated fire rings. Cookstoves fueled by butane or propane are permitted.