Crossing the Vasari Corridor, which was obviously designed by Vasari, is an experience that I absolutely recommend, but don't forget to make reservations in advance. The Vasari Corridor is the long passage that connects the Uffizi with Palazzo Pitti and passes over Ponte Vecchio. If you are curious to see the faces of the great protagonists of art history, this corridor offers the largest collection of self-portraits in the world: around 1,500 of them by artists that were painted from the 1500s to the 1900s.
FUN FACT: the Vasari Corridor was the only way to pass from the north to the south of Florence on liberation days. This can be seen in the movie Paisà by Roberto Rossellini, where the protagonist crosses the Uffizi Gallery full of packaged statues.