As others have noted, all campgrounds on the northern Outer Banks (Ocracoke north to VA state line) have a row of dunes between the ocean and nearest campsites which limit direct views of the water. I also think you'll find the 'tight' site size applicable to any of the commercial offerings and this closeness will be exacerbated due to your visit being in prime season.
If a water view is important, some campgrounds offer sound side sites that are directly on the water - Camp Hatteras in Rodanthe and Frisco Woods in Frisco are two that come to mind. Another option is the National Park Service Campground in Frisco. A few of the upper sites there afford a good view of the ocean albeit from a distance of a quarter mile or so.
There are no state parks on the Outer Banks; all public campgrounds are Federal. Cape Hatteras National Seashore extends from Nags Head to Ocracoke with several breaks for small towns or villages and offers four campgrounds. From north to south - Oregon Inlet, Cape Point, Frisco and Ocracoke. Friso is located within wooded rolling dunes and has many large sites with a good bit of privacy. The other three have fairly large sites but are located in open 'fields' with no vegetation separating them. Google Earth should give you a fairly good idea of their layouts.
NPS Frisco CampgroundWe now often stay for a week or more at one of the NPS campgrounds with Frisco being our favorite but, when our daughter was young, we used one of the commercial facilities (KOA, Camp Hatteras or Frisco Woods) for their hookups (AC can be nice) and activities for kids.
Drop me a PM with the types of activities you enjoy and I may be able to make some useful suggestions. Whatever you do, be sure to take the Hatteras to Ocracoke ferry - it's free and a unique experience.
Al