A.G. -
My favorite publics in the Birmingham area are Limestone Springs (Pate, in Oneonta, about 40 minutes from town), Timberline (Pate, about 30 minutes south on I-65), Ballantrae (Cupp, also south of town about 30 minutes) and Farm Links (Hurdzan/Fry, in Sylacauga, about 45 minutes south off of U.S. 280). Gil Hanse's Capstone Club is an interesting course and worth seeing also (it's about 45 minutes from town, off of I-59 toward Tuscaloosa), but they have historically had maintenance problems over there. There are three Trail courses here, including the one at Ross Bridge where they now play a Champions tour event, but they are not my favorites, and I would recommend any of the above before them. Depending on where you're staying and what time you have available, though, they may be your best option.
Depending on the day(s) you have available, and if you're looking for company, I'd be happy to take you out to Greystone GC, or there might be other private options if you're interested. Or I'd be happpy to play with you at one of the publics. Feel free to let me know here or IM me.
John