There's nothing special on the drive from Atlanta to HH. You might want to stop at a restaurant at any of the interchanges, but there's really no points of interest on the way.
Are you also considereing just catching the shuttle flight from Atlanta direct to Hilton Head Island? I don't know what it might cost, but if you did get a good price, it would save you the hassle of the Atlanta airport, and the drive. Then just rent your car at Hilton Head. The HH airport is very small and convenient.
Don't even consider taking a shuttle flight from Atlanta to Savannah as that wouldn's save you much as you'd still have an hour's drive from there to get to HH.
Charleston would be quite a bit out of your way but if you have a place to stay for maybe a day or two, it's a very nice city with lots of history. So if you do decide to drive, it might be worth it to you to add a few extra hours extra driving to stop at Charleston, either going on the way to HH or when returning to Atlanta.
We're just back from HH. The
DVC staff there has been making some program changes that they'll be putting into effect soon. The weather was great.
Have a great trip.