It is a very nice drive, and there are numerous places to drive on the beach, as well as camp. Starting from the north, there is Carova, which is an area where there are houses and trails to explore, all on the sand. From Carolla, there is about 10 miles of sand driving to the VA border and a natural area where you have to stop. It is very neat to see the houses and wild horses roaming, all while not seeing any pavement. Not aware of any camping on the beaches of Carova, and it is busy with cars, and there are no showers (no official campgrounds). Going south through Coralla, through Duck, and into Nags Head....tons of restaurants, hotels, piers, but no beach driving due to the high volume of people on the beach. From Nags Head, you continue south on HWY12 headed towards Hatteras. You will get to Oregon Inlet first, and there is a campground there (State maintained) with tent sites and RV hookups, and a shower house. There are 3 or 4 beach accesses where you can drive out on the beach or park and walk. After crossing over the bridge at Oregon Inlet still headed south, things will get a little desolate for a while, with a few random beach accesses on your left. Some for driving out and some for walking out. Then you will hit numerous small towns...Avon, Buxton, Frisco,and some others, where there are campsites (KOA is one) and small independent hotels. Lots of tourists and fishermen in this area. Finally, you wil come to Hatteras, where you can take the free ferry south to Ocracoke (about an hour ride, no reservations, first come first serve) Camping, hotels, and restaurants there, but you may need reservations due to the limited number of accomadations on the Island.
I would visit Carova just because of the no roads and wild horses, Kitty Hawk and Wright Brothers Memorial, the lighthouses, enjoy driving on the beach, go to Ocracoke for the day and eat at Howards (not the BEST food, but neat atmosphere)
You can't camp on the beach at Cape Hatteras National Seashore state park, and the times you can be on the beach are limited. There are usually big signs at the entrance of each beach access ramp that lets you know what is going on.