Dreher Island on lake Murray just north of Columbia has a nice campground. I think they have a primitive area for groups like yours. It's slightly out of your way, but very nice. the boys will love it, I know mine never want to leave.
http://www.southcarolinaparks.com/dr...d/camping.aspx
Lake Wateree is smaller and less out of your way, but I don't think they have a primitive area. call the parks and see what they have to say.
http://www.southcarolinaparks.com/la...e/camping.aspx