Honestly one of the best things to do in the Lowcountry of SC is get in the car and just drive. Roll up and down 17 and check out Hampton Plantation(home of Archibald Rutledge), Old ST James Church, Mcclellanville (where parts of Forrest Gump was filmed, Mepkin Abbey(monks corner), Boon Hall Plantation on 17. As far as beach close to Charleston, hard to beat Folly.
