The Ponte Vecchio is the one everyone photographs and almost nobody reads properly, so this walk does it the right way: from the Uffizi courtyard, across the goldsmiths' bridge, and up to the palace the Medici built on the far side. Go in the morning, before the bridge fills shoulder to shoulder.
Start in the Piazzale degli Uffizi, where the river end frames the bridge and the Corridoio Vasariano — the Medici's private overhead passage — begins its run. Walk down Por Santa Maria, rebuilt after the 1944 bombs that spared the bridge alone, then onto the bridge itself. It has held shops since 1345, butchers until a grand duke wanted only gold beneath his corridor. Stop at the open middle for the river both ways, and the Benvenuto Cellini bust, where the lovers' padlocks keep reappearing.
Cross to the south bank and slip into Santa Felicita for Pontormo's Deposition, all pink and acid green, lit through a high window. Then the rusticated wall of the Pitti closes the walk. Sit on the sloping piazza; the C3 bus runs back from here.