We stayed in several FL Panhandle campgrounds in 2009 and were very close to the beach in each one. St. Joseph's State Park (near Port St. Joe, FL) and St George Island State Park (near Apalachicola) are both large parks that have both campgrounds and beaches, and Gulf Island National Seashore is a long strip of sandy beach along the ICW where at the time they were allowing overnight parking overlooking the beach.
In the two state parks we were in true campgrounds. You might want to reserve ahead of time. My notes say we got into St. Joseph's because Reserve America had screwed up that week's reservations and the place was deserted!!
Gulf Islands National Seashore has two beachside parking areas where, at the time, they were testing allowing RVs to park overnight. The spots were marked "RV Parking" and there was no one there (probably no one knew you could stay overnight there). We had a fabulous time - walk out of the trailer onto the beach. Not sure if they continued to allow overnighting there. If so, don't miss is, it's awesome.
I have a few pics of the area from two blog posts while we were there:
Florida Panhandle - Don't Forget the "Forgotten Coast" | Roads Less Traveled
(FL starts about halfway down this page)
Florida Panhandle - Emerald Coast Gems | Roads Less Traveled