A couple of comments from a SC homegrown.
The beaches of SC, especially around Myrtle Beach (both northward and southward of MB) are excellent as are the State Parks for RV’s. It’s a little bit of a ride from MB to just across the NC state line in a little town called Callabash, NC which has some of the best fried “popcorn shrimp”, oysters, and hushpuppies to be found anywhere.
A little further northward, about 2 hours from MB, is Wilmington, NC which is a historical port dating back to Revolutionary War days and has a great waterfront area for eating, etc. The beach there is not as good as is in MB.
Hilton Head doesn't have much beach that is publicly available and is also historical; it had a POW camp there for yankee soldiers. Today, however, it is beautifully green, overpriced and crowded (imo). DW and I routinely travel there to visit relatives but will most likely stay this year at Stoney Crest Plantation Campground in Bluffton, SC, which is close to HHead but on the land side of the bridge. I have not stayed at that campground before, but I hear good things (hoped to be true).
Link to Stoney Crest:
http://www.stoneycrestcampground.com/about/
Also, from Bluffton, it is both an easy trip northward to Beaufort, SC (note: not Beaufort, NC) which is also historical and has a beautiful port to visit, and southward to Savannah, GA, which is a must see place to visit – great historic restorations and riverwalk. St Patricks day, more or less, is a great time to visit if you don’t mind the crowds (but be careful where you park, especially at night).
If I were planning to go to Charleston, SC, on a day trip, I would try to ask one of the TM Trailblazers about their recent (I think) rally at James Island (near Charleston). Further away, but also a possible campsite location you might want to consider is at Santee State Park , SC. which is located somewhat conveniently off I95 a little south of Florence, SC.
Just some thoughts off the top of my head and obviously I am a fan of SC trips.