Charleston and Savannah are "sister cities" and have a lot of similarities.
Personally, I prefer Charleston. There's a little more to offer there, with the aquarium and plantations nearby. Shopping on King Street and the market are also great.
Savannah is also a neat city and is closer to the HH resort, which counts for a lot, too! If you don't mind waiting in line, you can visit Paula Deen's restaurant.
Another option is Beaufort, which is between HH and Charleston. It's smaller than the other two, but still has a similar feel. All three cities offer horse-drawn carriage tours and have wonderful histories, not to mention quaint shops and great restaurants.