I wrote about a beach in Itoman, Kitanashiro Beach, that serves not only for the purpose of great snorkeling as it's right on the beach and camping but could also satisfy your need to camp as well, as many locals do. I'm unsure about your definition of what a glorified park would be, but this is pretty minimal with just a public restroom. People will generally camp out of the back of their van or set up a tent.
I've not done a campfire myself, but I see no problem laying out a small one there and roasting marshmallows, though, a grill would probably be best just to avoid the mess to clean in the morning.
The general rule of thumb with campfires, anywhere, actually, is to keep them under control and to clean up afterward. Nobody likes nails and coals laying around from the night before.
A frequently asked question amongst people on Okinawa Questions pages and those interested in coming here is where to find a great camping spot on the beach.
Okinawa, being an island, has a lot of coastlines. Because of that, there are plenty of areas to set up camp. However, some of those...