2) Birmingham Museum of Art - a "free" art museum. The taste is eclectic, and the kids may find it a little dry - but with the right traveling exhibits it can be a treasure. Quite large for a free museum.
3) The Vulcan - is a iron cast scrlpure overseeing Birmingham. Neat but in a limited way - short trip, low admission price (rain could cause this to became a cancelled side-trip).
4) Museum of Civil Rights - a world class museum giving a real background and true facts concerning the civil rights struggles in USA. Many of these events took place near the location of the museum.
5) A concert, play, etc. - the Birmingham area is full of all types of night life. Broadway Across America, Alabama Symphony Orchastra, Concerts, etc. are all available in a degree similar but smaller than Atlanta. Admission prices have a wide range in these events, so be careful before committing a family of 5 to one of these events.
6) As an after thought - the Alabama Sports Hall of fame is located in this general location. You probably need to be a sports fan with a good knowledge of Alabama ties to sports to fully enjoy the experience - but it is interesting and well priced for those fitting the situation.