There are four NPS CG's along the OBX. None have hookups. Yes, you can run generators, but hours are limited. The dump station at Oregon Inlet is across the street in the marina, as said. The one that serves both Hatteras & nearby Frisco is near Hatteras Lighthouse. I've never used the one at Ocracoke, but I'm pretty sure there is one. They have water points in the CG's near the bath houses and at the dumps. Last year, it was $20 / night.
There are several commercial CG's along the OBX, mostly in the Hatteras area. They have at least electric hookups. Rates are higher.
Jim, "Mo' coffee!"