I'm an ASM in charge of the outdoor program for a scout Troop in Chapel Hill, NC. Because we have very good options in the central part of NC we have no need to take long road trips to SC though I'm sure what I'm going to tell you applies to that state as well. There are several approaches to do flat water in Carolina. Lake/Reservoir, "Black water" swamps & rivers, Coastal tidal marshes.
LAKE/RESERVOIR: There are several State Recreation Areas that are on large bodies of water throughout the state. These areas have several campgrounds some with lake shore campsites that would allow you to shove off and explore right from your drive in campsite:
Jordan Lake, Kerr Lake, Falls lake, Badin Lake Area (part of Uwahrrie N.F. east shore of Lake Tilley) all in central NC allow this option. Falls Lake has access to the Three rivers Area (don't confuse this with a white water area north of Greensboro near Edan, NC) in eastern Durham County near the city of Durham. The Little, Eno, & Flat rivers converge on the Neuse river for a short run into Falls Lake north of the city of Raleigh. You could put in near Durham and paddle to a campsite at one of the campgrounds for a really great time.
BLACK WATER RIVER: Merchant's Mill Pond S. P. is a cypress swamp connected to Lassiter Swamp with has Bennet's Creek running through it. You can access paddle in campsites at the State Park. Be sure to bring a compass it's easy to get disoriented if you explore off trail.
Lumber River Canoe Trail is a 126 miles of black water river through 5 counties in the Sand hills region of the state. Some areas of the trail are part of the Lumber River S. P. where you can access river side camping. The Roanoke River Trail has a series of tent platforms for camping. It is part of the Albermarle Trail System made up of 29 separate marked paddle trails in 6 Eastern counties.
COASTAL MARSH: Two places I can think of off the top of my head with access to camping
Cedar Point Campground in Croatan N.F. with access to tidal mash paddling.
Hammock's Beach (Bear Island) S.P. an ocean barrier island which has some paddle up campsites on the back (sound) side of the island. If you don't mind a little backpacking you can leave your water transport at the ferry landing and hike the beach road 1+ miles to unbelievable ocean side campsites in the dunes. In season the ferry runs every 1/2 hour and there is an ocean side bath house with water and hot showers as well as a protected beach with life guards!!
You should consider contacting the Army Corps of Engineers who maintain reservoirs throughout the Southeast. They run campgrounds as well which would give you the option to camp & paddle. Check out local outfitters and paddling clubs who are very savy about the best or little known areas to do flat water. The Carolina Kayak Club's emphasis is on flat water paddling. The Bible of Flat Water paddling is "
Paddling Eastern North Carolina: a guide book for regional paddling."
Hope this helps you enjoy our great state.