I live in Bluffton, the town just to the west of Hilton Head Island. There is no dramatic burst of fall color like you would associate with New England. There is some color as we have some oaks and wild vines which do lose their leaves. The vines do turn a pele yellow in early December and the oaks' leaves redden before they fall, but this a subtle change.
There are many reasons to visit the area, but fall foliage just isn't very high on the list.