Climb the Duomo or Campanile. Traverse the winding staircases inside the duomo or the nearby bell tower to see some of the best views of Florence. Not only can you see the Tuscan countryside in the distance and the impressive palaces and churches of Florence in the fore, but it also shows you just how large the Duomo is. edit
Stroll the Boboli Gardens. These extensive gardens behind the Pitti palace provide excellent views of the city of Florence and numerous sculptures in a relaxed environment. Stop in the hilltop café, grab a drink and a seat outside and enjoy the view.
Street Performers by the Uffizi, in front of the Palazzo Vecchio. In the evenings street performers often put on a show here. Performances can range from violin duets to people dressed as sculptures. A nice place to stop while you eat your after-dinner gelato.
View from Piazzale Michelangelo
Enjoy the view from the Piazzale Michelangelo. It's a big square on a hill, but somewhat distant from the traditional tourist sites. It's easy to reach it even on foot using the stairs called "Rampe di San Niccolò". They are on the side of the Arno river just in front of the national library. Do this thing during the summer and during the night to admire Florence's lights.