I say avoid the Atlanta traffic at all costs, no matter what. You are taking your life in your own hands driving anywhere in Atlanta, and nowhere in the city is that more true than on 285. Stay off of 285. It will preserve both your safety and your sanity. People on 285 drive like wild crazed idiots that have absolutely nothing to live for and they have no regard for anyone else's safety either, and they are some of the rudest drivers I have ever seen.
That being said, if it were me I would go ahead and come on into Georgia on I-20, it does run through part of the extreme southern side of Atlanta near the airport, but you should be OK there. Then take I-75 south to Macon, about 75 miles away, then head through Macon itself, do not take I-475 and go around Macon, then I-75 will split off and you take the I-16 fork that will take you all the way to Savannah, it dead-ends into I-95, take I-95 north just about 15 miles or so and take the second Hilton Head exit, Highway 278 and it will lead you straight onto the island, about 30 miles away.
I have driven in Atlanta on 285 and the other interstates there a lot. I used to live there and I go up there to visit my family fairly often. Each time I drive on 285, 685, 85, 75, or any of the other interstates there it is worse than the time before. A friend of mine once said, "You better get right with God before you go driving anywhere in Atlanta". And he was right. Taking I-75 to Macon and I-16 to Savannah is much safer and a lot more peaceful. I-16 is downright boring. Not much there to look at and really not that many exits, either. But it will get you to Savannah and I-95 alive and in one piece.
Have a safe trip and enjoy your time on the island. Be sure to check out Harbor Town, South Beach and have dinner at the Crazy Crab at least once. Also have lunch at the Salty Dog. Hilton Head is a very nice place to take a vacation, this time of year especially since it is not so crowded and the weatehr is comfortable. I have been to HHI a lot, some of my family have time shares there. Reading this post makes me want to go back. Have fun on the island.