As long as you may legally possess a handgun and are in the country legally (obviously these two criteria go hand in hand), you may carry your handgun openly. There are a few places where you may not carry at all such as court houses, school grounds, except when dropping of and picking up children (stay in your car and keep if concealed when doing this), airport terminals, etc. For a better and more complete list, check out VCDL.ORG and join up while there.
You'll quickly find that Virginia is probably the most gun lenient and gun friendly state in the South. Look for get togethers in Richmond and its surrounds... there are frequent breakfasts, lunches, and dinners OD folks put together and they are excellent venues for you to ask questions and be made to feel comfortable OC'ing in your area.
BTW, Charleston is a beautiful city as is the state of South Carolina, in particular the low country.