We are not KOA fans, but we did stay at a KOA in Mt Pleasant once during early spring. Lakeside site, FHU and wide site. Very nice staff. However if you are into Old Charleston, this may not be the place for you. It is a drive from there across the river and into the Battery area.
We have also stayed at James Island. Lot of bugs and mosquitos there (we were there with a group in the summer) It is also a long drive into Old Charleston.
Prices will be better at James Island. Food (seafood) is closer and better in Mt Pleasant (IMHO) at Shem Creek Inn, Red's Ice House and a couple more right in that immediate area. Patriot Point is a good place to spend several hours wandering around the ships and museum and grounds. On the Mt Pleasant side of the river.