So you need to check with Bullseye range in Cumming (400 exit 13),
and that new indoor shooting range in Roswell,
and that new shooting range in northern Sandy Springs just below exit 6 off 400.
And you can also use backroads to get over to theHwy 5 / I-575 corridor and still be within an hour of Hi Caliber, Big Woods Guns, and Georgia Firing Line (formerly Nick's and formerly Ed's).
I don't know if any of them have a .22 pistol league. Well, I know Hi-Caliber does, for open-sighted .22 handguns. They meet on the 1st and 3rd Wednesdays of each month, starting at 7 pm.
Finally, you are probably just under an hour away from Riverbend Gun CLub (www.RBGC.org) and every month, on one Sunday morning or afternoon, they have an outdoor slow-fire bullseye pistol match. That match involves shooting at 50 yards, if I recall correctly. Fresh air and sunshine and nice country roads getting to and from there.