There is a great campsite, The Rock, just past Rockmart heading toward Atlanta. They have showers and other facilities, as well as being close to Rockmart for convenience.
There is a sign on the trail marking the turn off. It will take you on a gravel road and you then have to cross GA 278. That would put you about 2/3 of the way to Atlanta, which might be more than you were planning to ride for that day, but it's worth it. Also, the ride from the Silver Comet to Atlanta proper is a more challenging ride.
What is your final destination in Atlanta? I may be able to help with some advice on that portion, as well.
Tommy