Women should take the same precautions they would take anywhere else. Many women traveling to this region have to adjust to the prevalence of traditional chivalry. In the South, if a man opens a door for you, it’s considered a sign of respect, not condescension.
Another adjustment is the possible assumption that two or three women who go to a bar or tavern together might be there to invite male companionship. This misunderstanding can happen anywhere, but in some parts of the South it might be slightly more prevalent.
While small towns in South Carolina [1] are generally very friendly and law-abiding, some are more economically depressed than others and hence prone to higher crime. Always take common-sense precautions, no matter how bucolic the setting may be.
Links:
[1] http://www.moon.com/destinations/south-carolina