This won't be a comprehensive list, but I would include:
* a visit into Sea Pines to go to Harbour Town and the South Beach areas (where you can purchase the requisite Salty Dog tee shirt), and maybe Lawton Stables;
* a visit to the Coligny shopping area
* the Tanger Outlets in Bluffton
* Old Town Bluffton is kind of fun
* maybe a visit to the natural museum on the Island that, I believe, is near Jarvis Park
Have fun! Hope you don't swelter!