Matanzas jeep club is based out of St. Augustine. I know they go to a place out there that was a failed housing area. I can't seem to remember the name of it off my head right now.
There's also a couple of clubs in Jacksonville that do regular rides out to Osceola national forest. A lot of the wheeling will probably slow down right now though since its hunting season and some of the forests are officially closed for just riding in.