Museo Galileo

The finest scientific-instrument collection in existence, blissfully uncrowded. The stars: Galileo's two surviving telescopes and the very lens that found Jupiter's moons in January 1610 (he named them the 'Medicean stars': history's most effective grant application).

Also: his geometric compass (the pocket calculator he manufactured and sold), the room-sized Santucci armillary sphere, the gorgeous glassware of the world's first experimental-science academy, and, in a reliquary jar, Galileo's middle finger, pointing eternally upward at his inquisitors.

The column outside is a working 17th-century sundial; check your watch against it.