We got to Hilton Head every year because my parents retired there. There are always tons of people from Ohio there, so I guess the drive can't be too bad. I'm not sure if I would call it quiet and quaint, but it is nothing like Myrtle Beach. It really is lovely, but there is also a lot to do, especially for families.
DH and I went to Block Island, RI for a few days before we had kids and loved it. We both thought it would be a great place for a family vacation. You could go there and stop off wherever you used to live in RI to visit old friends.