I know this is a seriously late reply, but for anyone interested, I'll add what little I know.
First off, yes, there is a nice campground right at off the end of Billy Mitchell airport on Hatteras Island. My wife and I have landed there, hiked over for tent camping and flown out the next day. It works just fine. It is about a one mile hike but beach people are generally very friendly and will almost always pick up a hitchhiker to shorten your trek. When we were there, they were doing the ole water conservation trick of turning off the hot water to the showers, so if this is a dealbreaker, be sure and ask when you call ahead to check availability. One huge plus is that the campground is only one dune line away from the ocean, so its a very short walk to get wet and salty. Be sure and look both ways since the beach here is open to driving and its is a very popular spot for surf fishermen. If you get caught short on supplies, there is a nice hunting/fishing store about 1000' from the south ramp called Frisco Rod and Gun where you should be able to find most anything to get you through your adventure (cold beer, sunblock, high power deer rifle, pretty much anything you could think of).
Don't miss a day trip over to Ocracoke Island. Its only 20 miles from Hatteras to Ocracoke and its a beautiful flight. When announcing on the unicom frequency, feel free to follow the local custom and ask Howard's Pub for a ride into town. They will drive out to the airport and bring you back in their open air electric vehicle (don't call it a golf car, they are touchy about that for some reason). If you like walking, its only about 3/4 of a mile. Howards offers good food and libations, so its a great first stop. From there, there are several vendors who can rent you a bike or golf car to drive around and explore the village, and when you are done, Howards will take you back to the airport if you like. As is the case with most service workers in tourists areas, the drivers appreciate modest tips.
For either destination, keep a few things in mind. Ocracoke, Hatteras, and First Flight up at Kitty Hawk are operated by the Park Service so they don't offer any services, including fuel, and night operations are not permitted. Fuel is available at Dare County Regional and Currituck County. Both are reasonable and friendly. Take mosquito repellent just in case the breeze falls out. Be sure to visit all three of the park service airports, they are a must for anyone passing through the area. Wash your aircraft well when you leave, including inside the engine compartment, underneath, etc. It will get salty.