Are you speaking of Birmingham, Alabama, or Birmingham, England?
If you are speaking of Birmingham, Alabama, it helps to know what part of the city you're looking in. If you're in Shelby County, there is a place at Lee Branch called the Melting Pot. It's a fondue restaurant; slightly pricey, but well worth it, I've heard. If you're closer to the city, you can travel to Bessemer and eat at the Bright Star restaurant. It has a rich history and their Greek dishes are their specialty (not a Greek restaurant; they serve steaks, pasta, chicken, and lots of seafood).
Hope I helped!