doors at the Baptistery in Piazza del Duomo, take a spin on the carousel in Piazza della Repubblica, see where Michelangelo was buried at Piazza Santa Croce , admire Brunelleschi's Ospedale degli Innocenti in Piazza Santissima Annunziata, mingle with locals in Piazza Santo Spirito 's low-key cafes, and hang out with David