Im in Birmingham and live in Hoover. Hoover is pretty big suburb, so depending on what side of town you are on J Clyde is a must stop. BTW the cabs kind of suck, so, sorry about that. Make sure you use Yellow cab, they seem the best and the "cleanest". If you don't want to leave Hoover the best place to go is On Tap at the Galleria, they have the best beer selection this side of town. Also Charlie's Tap House is in Hoover too (old On Tap Location) and it's pretty cool, but they allow smoking so it can be at times, smokey.
If you're willing to venture in to downtown Birmingham (which you should), hit up The J Clyde and in walking distance you could go to Dave's and World of Beer if that's your thing. I recommend just living at J Clyde though.
Some of the Breweries are open too. Good People and Avondale are both open 7 days a week. I think you will find the better beer at Good People, but depending on your taste Avondale might be your place. Avondale has a bunch of places around it. Post Office Pies (pizza), Parkside (bar), 41st Aircraft Sales (bar), Saw's Soul Kitchen (best BBQ in town). Cahaba is open starting on Wednesdays, so I dont think you will be in town. If you can make it to Hop City, they have an awesome selection in bottles as well as a draught list that is pretty damn good. You can sit and have a pint and shop around of bottles and/or cans.
HTH. Let me know if I can help any further.