Another must-see is the museum right next to the dome, the Museo dell'Opera del Duomo. Inside is one of the most amazing things I've ever seen--the hand-cast "Gates of Paradise" doors of the Baptistery, by Lorenzo Ghiberti. Simply incredible!

Fun fact about Ghiberti and the doors he made: he won a contest in 1401 to create the first set of the doors. The runner-up? Brunelleschi.