The Palazzo Vecchio is one of the more famous in Florence and was a Medici Palace. The sculptures outside include Ammannati’s Neptune’s Fountain and Perseus by Cellini. At the Church of Santa Croce see the tombs of Machiavelli and frescoes by Giotto, and at San Lorenzo the ceilings were designed by Michelangelo in what was the Church of the Medici.
Around the Piazza Della Repubblica look for shops with perfumeries and soaps with centuries of tradition, and take a coffee in the square to watch the world go by. For an excursion try Fiesole and relive the scenes from “A Room With A View”, or travel to nearby Pisa for the famous Leaning Tower and the Duomo.