One of the most beautiful campsites on the island is this, Camping Paraiso. It is located near the beach in Palmas, and practically has its own private beach. You can get there by road or by boat. There are showers, shade, restaurant, bar and public tour packages on sale. Sometimes they have parties, too. From here, you can hire a speedboat to get to any point on the island, or walk to the beach of Lopes Mendes.
In addition to the Camping Paraiso campsite, which I've already described on Minube, this is another option for camping in Palmas. The owner, Alexandre, is super helpful. Next door is a restaurant, Fani, and there are other restaurants, too, if you walk in the opposite direction. The campsite is near the exit road to Abrao. It has clean toilets, showers, and awnings to protect from the sun and rain.