Florence pulled most of its walls down in the 1860s to make boulevards, the way every ambitious city did. But the hill above the Oltrarno kept its defences — the fort, and the longest run of medieval wall left in the city. Walk both, high up, with the whole place spread below.
Three and a half kilometres, best on a clear afternoon. From the Ponte Vecchio, climb Costa San Giorgio to Porta San Giorgio, then turn into the Forte di Belvedere — a six-pointed star the Medici built in the 1590s to keep an eye on Florence as much as to guard it. The grass ramparts give you everything at once: duomo, tower, hills, river. There's usually a sculpture show in summer, and entry's free when it's on.
From the fort, pick up the medieval wall and follow it down the hillside — crenellated, climbing, almost empty of people. It carries you to Porta Romana, the grand southern gate where the road to Rome began. Bus 11 back across the river from there.