If you want to do one touristy but wonderful and cultural thing in Florence, go to the Museo di San Marco (on the right of the church, open MORNINGS – weekends are dodgy: check by clicking the website above!) which is filled with frescoes by Fra Angelico from the early 1400s and Ghirlandaio's huge Last Supper in the refectory but, more excitingly, upstairs are the 44 tiny cells for the resident monks in the C15th with a devotional fresco each, and you can see Girolamo Savonarola's cilith (à la Da Vinci Code), his habit, his chair and pictures of him with his amazing nose... all rather creepy because (according to some) he was a bit of a religious dictator later burnt to death in the Piazza della Signoria (see the plaque in situ by the fountain). There are two pretty little courtyards there which are lovely, cool places to sit and read...