My daughter and I spent all afternoon at the Birmingham Museum of Art. It's our favorite way to spend a day together and most of the time (believe it or not) I have to drag her away.
I may have some bias, but I think it's the best museum in the southeast by far. The collection is huge and the work spans all of art history.
My daughters favorite gallery is the 13th and 14th century Italian work. She is familiar with the stories behind the biblical iconography. She also enjoys the european biblical narrative paintings from slightly later for the same reasons.
Her individual favorites in the collection include the giant Bierstadt landscape and the Sargent portrait. We both think that "3 for 5" is in the top 5 too.