Birmingham has some of the best food!
First of all, Jim & Nick's, even though it's a regional chain, has the best BBQ, but really, I go for the cheese biscuits.
There is also a fantastic mom & pop Italian joint at Five Points called Ranelli's Deli. It looks almost like a gas station, but it's just good, very inexpensive Italian and sandwiches. Reminds me of the Hill in St. Louis. John's City Diner is also one of my favorite places (on Richard Arrington Blvd at 1st Ave N). Great gyros at Al's (on 10th Ave S at 17th St S).
There is a good rock climbing gym that just opened up called First Ave Rocks, if you're looking for something different. It's not far from John's City Diner. The art museum is very nice, and if you have access to a car, the Tannehill Iron Works (state park) is outside of the city and is a great place for a hike. It's very beautiful, and they have some fantastic archaeology going on there, both more recent and prehistoric.
ETA: Smoking is not prohibited in most of the US. It's just a few states that have bans in effect.
[ Edit: Edited on 12-Aug-2009, at 11:06 by rbyslipahs ]