Start very early in the morning with a visit to the Cathedral square, where the Dome, Giotto's bell tower and the Baptistery stand, take your time and head to the Accademia Gallery, a must-see for anyone who's in love with Michelangelo Buonarroti (the original David is currently housed here).
Head toward Piazza San Marco and turn left into Via Cavour, walk up until you find Canto de' Medici on your right and follow it through until you see the Basilica di San Lorenzo; look for a restaurant in this area and visit the Church and the Medici Chapels later in the afternoon.
Head over to Via dei Calzaiuoli and follow it through until you see Orsanmichele on your right, turn right after the Church and turn right again into Via Calimala in order to see Piazza della Repubblica, that corresponds to the ancient Roman forum and old ghetto. Do your shopping between Via Roma, Via degli Strozzi, Via Tornabuoni and Via della Vigna Nuova and don't forget to check whether there are temporary art exhibitions you might be interested in at Palazzo Strozzi.
If you're very hungry we recommend you find a restaurant in the area, otherwise you can always cross the bridge named Ponte alla Carraia and look for a less touristy restaurant in the San Frediano neighborhood.