On the river next to the Uffizi in 12th-century Palazzo Castellani – look for the sundial telling the time on the pavement outside – is this state-of-the-art science museum, named after the great Pisa-born scientist who was invited by the Medici court to Florence in 1610 (don't miss two of his fingers and a tooth displayed here).

A visit of the museum unravels a mesmerising curiosity box of astronomical and mathematical treasures (think telescopes, beautiful painted globes, barometers, watches, clocks and so on) collected by Cosimo I and other Medicis from 1562 and, later, the Lorraine dynasty. Allow plenty of time for the interactive area where various hands-on exhibits allow visitors to discover first-hand how and why some of the historic instruments actually work. Temporary exhibitions are equally compelling. Save your ticket to get €3 discount on admission to Museo di Storia Naturale – Zoologia La Specola.