If you are looking for a square to laze about and enjoy the Tuscan sun, head over to Piazza Santa Croce. It is the other large square in Florence, but much less busy compared to Piazza della Signoria. A beautiful church - Basilica Santa Croce - the largest Franciscan church in the World, overlooks the rectangular Square. The square is surrounded by several important palazzos that are great examples or Renaissance architecture.
The square is also an outdoor art market. There are many artists showing and selling their work. Some of the smaller paintings of Tuscany would make great gifts or souvenirs.