We live about three miles from Tops'l State Park RV Park. I will second that recommendation. It is one of the nicest RV parks, public or private, that I have ever seen or camped in. The campground is actually located in Santa Rosa Beach, which is about ten miles east of main Destin. There is a lot to see and do in this area.
Moving west, the Biloxi/Gulfport area has a lot to do and see. There are several nice campground down by the ocean. Go on Woodalls, RV Parks - RV Camping & Campgrounds
and take a look.