João Pessoa has a fair number of campsites in and around the city, almost all of them are on the coast near the bigger beaches, mostly they’re near cities rather than in out-of-the-way places.
They will usually have basic facilities, running water and toilets, perhaps a simple restaurant and are popular with young Argentines and Brazilians.
A few fancier sites in João Pessoa are designed for people with camper vans or big tents in the back of their cars. Having your own tent, or hiring one, is also particularly useful in ecotourist regions, where it can really open up the wilderness to you.
In all cases, however, the problem is security, partly of your person, but more significantly of your possessions, which can never really be made safe. Great caution should be exercised before camping off-site – only do so if you’re part of a group and you’ve received assurances locally as to safety.
Stay safe camping in João Pessoa!