For several centuries of its history Florence turned into one of the most beautiful cities in Italy. And even at the background of such great cities as Rome or Venice, Florence takes a worthy position among all other important tourist destinations.
You can most fully feel the spirit of late Middle Ages or Renaissance in the city. As Florence then was a kind of cultural & scientific center. There lived and worked almost all great Italians of the period, from Dante Alighiery to Leonardo da Vinci.
One of the most important sights of Florence is the huge cathedral of Santa Maria del Fiore, which dominates all the buildings of the city, exceeding their height by nearly two times. The cathedral and bell tower is a wonderful example of Italian Renaissance architecture. So, you should visit it in the first place. Also, you should climb atop Giotto Bell Tower to admire the dome of cathedral and views of Florence.
The oldest square of the city, Piazza della Signoria, is only two quarters off the cathedral. It is dominated by the Palazzo Vecchio (Old Castle), and on the square itself you can admire sculptures of Florentine masters, such as Michelangelo, Donatello, and Cellini, etc. There is an alley between the Old Castle and Lanzi Gallery leading to the famous Uffizi Gallery. If you have enough time and patience to stand in a queue (and it is very desirable), you will get a great pleasure of your visit.
After a tour of the old quarters of the city, you may have a stroll along the Arno Embankment. It gives you a beautiful view of the Old Bridge or Ponte Vecchio. Beyond the bridge there is Pitti Palace, one of the largest palaces in Florence. To save time you may not get inside the palace (as its gallery is incomparable with that of Uffizi), but you are sure to look around the Gardens of Boboli.
It would be a blessed place for almost any tourist who has just made a tour of the streets of the city. The terraces of the garden let you climb the hill, giving a wonderful view not only of Pitti Palace but also of the entire city. From the Gardens of Boboli you need to pass to the hill, and then climb onto Piazzale Michelangelo. It just from there that you can have the most magnificent panorama of Florence.