The Piazza della Santissima Annunziata is where the Renaissance worked out how a public space should feel — three matching arcades, a bronze duke on a horse, and Brunelleschi's foundling hospital running down one side. Architects still argue it's the most balanced square in Florence, and from under the central statue it's hard to disagree.
About two and a half kilometres, good in the late afternoon when the arcades throw long shadows. Start in the square, then read the Ospedale degli Innocenti loggia from the pavement — the 1419 building usually called the first of the Renaissance, with della Robbia's blue babies above the arches. At its left end, find the wheel: the barred window where infants were left, anonymous, on a turning drum. It quiets you.
Step into the basilica for five gilded minutes, then walk out down Via dei Servi, which frames the cathedral dome dead ahead — keep your eyes up. Through the university quarter and Piazza Brunelleschi, and it's a flat walk to Santa Maria Novella and the train.