If you're flying, Birmingham is probably your best airport option. You could get 3-4 rounds in at Ross Bridge (18 holes), Oxmoor Valley (36 holes), and then drive over to FarmLinks for a day. It's about an hour drive from Birmingham.
You could fly into Montgomery, but that would most likely involve one or more connecting flights. There you have Capitol Hill (3 courses), but based on the info above it sounds like some may be closed for renovations.
Last option would be to fly to Atlanta, and then rent a car and drive 2 hours to Auburn/Opelika, AL. Grand National has two, 18 hole course and an 18 hole "short course".