Depending on when you are traveling......
Holly Shores Campground on US 9 off GSP Exit4. Then maybe 10 miles to the Cape May - Lewes Ferry.
Down US 113 and US 13 through Delaware to Maryland then over to Assateague National Seashore just outside Ocean City, MD
Follow 13 down over the Chesapeake Bay Bridge Tunnel and into Virginia Beach. From there you can head out to I-95 or follow US 17 South to the Outer Banks or all the way down to Myrtle Beach and Charleston.
For that matter, from Charleston to Jacksonville, 17 isn't a bad road to travel. Not as fast as 95 but a bit more interesting. Of course YMMV.
X2 on James Island County Park
To go by way of Baltimore head East on US 50 from Ocean City area and over Chesapeake Bay Bridge.
Safe and happy travels