We have stayed a couple of times at Camp Hatteras on the sound side. Its pricy and in summer it will be full of kids and families. Not far from there is Ocean Waves campground. No pool and all that kind of stuff - its a very small campground but much less expensive. We've never been able to get reservations during the times we were there but that would be a good choice. We have some friends that like Frisco Woods further south. Its on the sound side.
If you have a 4X4 you can go via one of the beach access roads and drive down the beaches. A permit is required now from the NPS, but its still pretty cool to be able to drive a few miles from the beach access and set up your beach chairs and umbrella with no one else in sight.
And as menitoned by others, Ocracoke is a very neat place to spend a day or so. We've never camped on Ocracoke but its an easy day trip from Hatteras.