Experience of driving through every year at this time since the Runoffs in '82 from every direction except north. The only time the traffic was clear, and I sailed through Atlanta was coming from Montgomery on I85 at 0300. The traffic was light, but I had to speed up to 90 to keep up!
If it rains, or if there's an accident, bring a sandwich, a soda, and a pee jug. You'll be there for a long, long time.
In variably, we hit town about 1500 and stop. I've tried coming from Montgomery up I85, 285E, and 285W. Don't recommend any of them.
I come through Birmingham on 20 and usually get off on 285W, but that can be an incredible hassle as the entrance ramp is short, tight, and usually blocked with trucks. Last year, and probably this year, we'll go to I85 through town. Oddly, it seems a little faster. At least the exit is easier to negotiate with a trailer and a caravan of crew vehicles.
Coming from the north would be much easier, as the track is about an hour north of Atlanta.