Times have changed, that's for certain. My father (born/raised in Columbus) found a beautiful arrowhead on the Chattahoochee banks when he was a kid ... in the late 1930s. It was lost sometime in the mid 1960s ... what a shame.
The Columbus area was Muscogee/Mvskoke/Creek territory (until 1825~36) and there are all sorts of creeks and swamps in the vicinity (I am an alumnus of "Benning School for Boys"). Names such as Muscogee, Chatahoochee, & Coweta Counties, Koweta and Cusseta are named for former occupants.
Perhaps you could look along the shores of Lake Oliver? It is an artificial reservoir, and I'll bet stuff can be found. [I found some points at "Land Between the Lakes" (same type of reservoir) in Kentucky/Tennessee when I was stationed at Ft. Campbell back in 1982.] You might also try the Flint River, which is about 40 miles east of Columbus.
--ghp