Your seven and eight year olds might enjoy the Wright Brothers Memorial history site, where the Wrights did the first flight. All the kids would like to fly kites on the beach so take one or buy one at Kitty Hawk Kites right across the highway from Jockey's Ridge....which is the largest sand dune on the East Coast and worth taking the family to climb!
Also, drive over to the town of Manteo (it's right next to the banks, very easy to reach) and take the kids to the great history center there devoted to the "Lost Colony" that disappeared. The history site has replica ships to explore and climb all over; an Indian village (or it did a few years back) and a pit where they can dig around for shark teeth! Three year olds may not have much attention for this site and your baby will need to be in a stroller or left with someone else but it would be good for the three older kids.
There is a great state park beach just south of Nags Head. Look for the state park on the map; you want the ocean side beach that has the dressing rooms and outdoor showers. It's away from the beach houses etc.
Also, the Currituck Lighthouse and the Bodie (pronounced "body") Island lighthouse are both interesting, though again, not appropriate for younger ones if you plan to climb.
I would add -- Cape Hatteras Lighthouse is magnificent but is very, very tall, and probably not a doable climb unless the older kids are really big on stairs. The 3-year-old -- no way.
There was a new nature center close to opening, right next to the Currituck lighthouse, a few years back. It must be open by now and should be great for kids -- check online!!
Enjoy!