dbw, if you are driving regularly to Alabama, you may want to look into getting a permit from a state such as Utah. You don't have to be a resident, nor to you have to go to Utah to receive a permit. You fill out a form and pay a small fee. Having a Utah CCW will make your Ohio CCW legal in Alabama via reciprocity. You can get the information from the Utah AG site.
I believe New Hampshire has a program similar to Utah that only requires you to mail a form and pay a fee for a permit that adds several reciprocity states.
With the number of cops along the highways in Georgia, it's wise to have reciprocity there if you are going to be driving through Georgia with a firearm.
Georgia DOES NOT have reciprocity with Ohio, but KY, TN, and FL do have reciprocity agreements with Ohio.