Obviously, several options are available here but I'm new to the area and curious to discover some favorite weekend flatwater and fishing in the area.
You might try Advice, Suggestions,
and General Help… or Paddlers Place Discussion forum.
I don’t know of anything high quality in the way of flatwater paddling in the immediate area around Columbus. I would probably go down to Reed Bingham State Park. There are some interesting creeks around there, but I don’t think you’d want to do them alone, in the winter! It would be funny to come down Mulberry Creek unsuspecting and suddenly encounter hard-to-portage waterfalls!
Check out the Coosa near Wetumpka AL, short drive from Columbus, further north is Hatchett Creek and the Tallapoosa, all in AL.
Hatchet has certainly been runnable
an unusual proportion of the time for autumn due to it having been so rainy. Kinda similar to Mulberry but no catastrophic waterfalls or rapids… Just some easy ones. Usual minimum for Hatchet is 600 cfs, and I wouldn’t run it alone with more than 1200.