Visit the villa of Giovanni Spadolini, Liberal Italian politician and Prime minister, newspaper editor, journalist and noted historian.  His villa  contains a vast collection of books and cultural artefacts, as does the library he left to the public.  The view is AMAZING, down the valley from Pian dei Giullari.  This is a very little known area of Florence, visitors are rare and dignified, all visits are booked in advance.  The villa is open weekday mornings.

Visit La Specola-Museo Zoologico, the city's natural history museum. Hurry through the fossils and mangy wildlife displays to the rooms that display the museum's collection of 18th century wax human anatomical models. These are what doctors once used to learn about the human body (when there was nobody around to dissect). Some - including dioramas of plague victims - depict unfortunate medical conditions; other show various aspects of healthy bodies. They are grotesque, masterful, informative and wonderful. The museum is on the other side of the Arno (the Oltrarno) just past the palaces.