I think you would like Devils Fork better than Table Rock in regards to spaces.
While in Charleston and visiting Ft Sumter take a visit to Patriots Point naval museum. We personally like Lake Wateree State Park as it is just 20 miles from home. Most sites are large, asphalt, decent separation. For your trip just a bit out of the way but not too bad.
And if you haven't been there, on your way stop of an take a look at Hunting Island State Park for a future or return trip stop.
Tom Wilds
Blythewood, SC
2016 Newmar Baystar Sport 3004
2015 Jeep Wrangler 2dr HT