Hanna Park is a great camping spot. The sites are generously sized and level. It's a short walk to an extraordinary beach that's never too crowded. At worst (4th of July?), walk a few yards from a dune crossover.
The park also has the best mountain bike trails in the area. Weekend mornings locals fill the parking lot at the entrance to ride, and the trails are empty pretty much the rest of the week. There are also hiking/running trails through the same woods to keep everyone separate.
Another biggie is the park has a gated entrance so you don't have problems with theft like some parks. The location is nestled between Mayport Navy base and Atlantic Beach, a tony beach town with several grocery stores, great restaurants and night life.