If you want to do a trail during the winter, you could try the Silver Comet/Chief Ladiga Trail, which nearly 100 mile long paved trail across Georgia and Alabama. It's a former rail line, so completely separate from automobile traffic and the grade generally doesn't get very severe as trains don't like steep inclines. Pic related is about as steep as it gets.
It's too bad the Alabama section doesn't extend a couple more miles into Anniston because there's a nice bed and breakfast near the Amtrak station where you could stay until the Amtrak Crescent comes through to take you back to Atlanta. For a city of its size and location, Anniston has a couple of surprisingly good museums. People who do the trail often will break it into two days, staying the night at Cedartown, Georgia, which has hotels that explicitly cater to cyclists.
https://en.wikipedia.org/wiki/Silver_Comet_Trailhttps://en.wikipedia.org/wiki/Chief_Ladiga_Trail