Greensboro camping is the pits, I would say the High Point lake(oak hollow CG) would be great.
Havelock,NC Stay on US 70 and cross the bridge on US17 from NewBern and stay at the KOA(Bridgeton) US17 just across the Neuse River from NewBern. Great place to stay great campground hosts. You are just a short drive to Havelock and the Morehead city and the beach on US 70. NO camping in Havelock or Morehead city areas.
At Myrtle Beach you are cutting it close to Labor day weekend rates and very full campgrounds around that area.If the big 4(ocean lakes, lakewood, pirate land, Myrtle Beach travel park) in the area are full check the MB KOA thats not ocean front or the new one Cypress Resort on the intracoastal waterway. Its off SC-544 which is right off US-17 bypass. get up and head on down US-17 to Charleston. There are 2 state parks in the area so you can see online reserve America if they have openings also. MB state Park and Huntington Beach State park.
Charleston I would say James Island county park.. Best around the area..that is local county park run by the county and its on a marsh inland from the ocean..It has a water park open to the public, well the whole park is but the campground is private to the campers..
Hope this helps..
if You stop in THE Greensboro area and you need help for anything let me know... I'll give you contact info for emergencies.. My neck of the woods..
randy