The Silver Comet/Chief Ladiga trail is a rails-to-trails route that runs from “almost Birmingham, AL” to “almost Atlanta, GA”. At this particular point in time, it goes 94 miles from Anniston, AL, to Smyrna, GA. More is being added. It follows the old route of the Silver Comet train.
Looking over the handlebars
There are lots of ways to ride it, but first a map:

Here’s the link to the page the map came from:
https://bikesilvercomet.com/default.aspx There is lots of good information here.
From Smyrna to Anniston (or the other direction), it can be a good century ride, a moderate two-day ride, or a very easy three-day ride. There are B&Bs, motels, and camping areas along the route.
Here’s a link to a tour that went out from Smyrna to Esom Hill at the GA/AL state line, and back.
https://www.lifeinthebiggreenjolly.com/silver-comet-trail-bike-tour/They are spot-on with just about every comment. This is what I meant by “not yet figured out how to cater to bicyclists.”
These folks did their ride using motels. There is also decent camping at Piedmont, Cedartown, and near Rockmart to my certain knowledge.
From Esom Hill to Anniston you may find this useful:
https://videos.kinomap.com/en/playlists/11789In spite of it being so well maintained and groomed that it looks like a daily commute, it runs through some pretty remote areas. Deer, bobcats, foxes, hawks - I’ve seen them all along the trail within 20 miles of Smyrna, and more frequently further out. I’ve found it to be absolutely safe for an older guy alone, but if you’re doing the whole route as a tour you should have a buddy. There is decent AT&T cellphone service everywhere along it that I’ve tried.
East of Dallas there are multiple bike shops, like:
http://www.boneshakerbicycles.com/, or:
http://comettrailcycles.com/ West of Dallas in GA there really isn’t a lot of support close to the trail. Anniston has:
http://www.wigswheels.com/ And while the trail probably could be ridden end-to-end with a road bike, a light tourer would be better.
There are some lovely places to stay. For example, in Anniston:
http://www.parkerbnb.com/ But it is also a good trail to try out your camping gear. There are well spaced facilities that are kept clean.
The real downside for a tour on the Comet is access. AMTRAK goes from Atlanta to Anniston, but won’t take bikes on or off at Anniston. Greyhound runs from Atlanta to Anniston, and bikes are $30 (plus $10 if you have to buy a box), but Atlanta’s light rail does not connect the airport with either Greyhound or AMTRAK. So first you have to get to/from the trailheads.
So far, no enterprising tour company that I know of has set up a tour and provided transport for bikes, but Comet Trail Cycles (above) supports short rides.
If you’re looking for a domestic trip to get your touring juices flowing, and that won’t dump you off in the weeds, the Silver Comet/Chief Ladiga Trail is a good ride. Being in the South, it is available in months when northern rides are too cold for comfort. It is also a ride to get your fully loaded touring bike checked out. For a “century” it is kind of ideal - limited grade, well maintained, access at either end, and just long enough.