Piazza della Signoria has been the political heart of the city from the Middle Ages to the present day. For a visitor, it is a free outdoor museum.
It gets its name from the most important monument there, Palazzo della Signoria, designed by Arnolfo di Cambio in 1298-99 for the seat of the Republican government. The palace continued to maintain this politically representative function in the city during the reign of the Medici and later under Duke Cosimo I, who lived here between 1540 and 1565, commissioning his court architect, Giorgio Vasari, to double the building in size. When the Grand Duke and his family moved to the new palace of Pitti in 1565, Palazzo della Signoria began to be known as Palazzo Vecchio (the Old Palace).
There is no admission to view the art and it is open every day all year around. We wandered around the piazza a number of times to gaze at the statues and bask in the sunshine. The square has a number of eye-catching statues, most famously, at the entrance of the Palazzo Vecchio, is Michelangelo’s David. The statue is a copy of David while the original is kept at the Gallery of the Academy of Fine Arts or Galleria Accademia, but that hardly matters when you look up at one of the most iconic statues in the world.
David is not the only statue to admire. Also in the piazza are the bronze equestrian statue of Cosimo I by Giambologna (1594); the Fountain of Neptune by Bartolomeo Ammannati (1575); The Lion, referred to as "il Marzocco", with a copy of the Florentine Lily by Donatello; Judith and Holofernes, a copy of the one by Donatello; and Hercules and Cacus by Bandinelli (1533).
Just off to one corner is the Uffizi Gallery and across from the Palazzo Vecchio is the Loggia dei Lanzi. Two more great art venues.
Benvenuto Cellini's statue Perseus With the Head of Medusa is in the Loggia dei Lanzi gallery on the edge of the Piazza della Signoria. This is another splendid open-air museum that evokes centuries of greatness and power.
This is an easy to do must do. You can wander around to inspect everything in the piazza or just relax at one of the cafes or gelaterias and admire from afar.