If you ask anyone in our family, they will tell you ANY time is a great time to go to Hilton Head!
Actually, it depends on what you want to do. If it's the beach, obviously, the summer months are the best, but they're also the most crowded and hottest. If you want the beach without the crowds and don't have school schedules to worry about, early September would probably work best for you.
If you want to golf, spring and fall are probably the best, since the weather in the summer can make it very uncomfortable.
The resort is beautiful at any time of the year -- even during the winter months. It's just that then it's TOO quiet for some people.
Whenever you go, have a wonderful time!!