I would stay put in one place rather than packing up and schlepping kids and everything from place to place. I would pick Kiawah or Hilton Head (confess I haven't been to Myrtle Beach), becuase they are also close to Charleston and Savannah, respectively.
Kiawah is really nice, but we also liked Hilton Head - plenty of things to do there as well. We hiked, rode bikes all over (including on beach) and went horseback riding. You can take a boat over to Savannah, which is really beautiful. But also with Kiawah you're very close to Charleston, which is also lovely.
Good luck and have fun!