With so much to see in Florence, it can take a whole day just to plan which spots you might want to see. Fortunately, all the major sights are located pretty close to one another. So whether you decide to take a rain-soaked day and visit the Bargello, or you want to know the full extent of the Medici family's wealth by stopping by the Pitti Palace.
Of course, it's impossible not to talk a walk across Florence's most famous bridge: the Ponte Vecchio. Not only is Florence a city with some amazingly intact pieces of Renaissance and Medieval history, but it also has traces of the modern world in it, as well. One example of this is the Strozzi Palace, where you can find modern art exhibits and a cafe below. It's a great place to stop when you've seen all the Renaissance artwork you can muster.
Even just walking the streets of Florence can provide you an idea of what things were like at various points in time. One of the best ways to know the city is to simply take a stroll with a gelato in hand--you're sure to stumble on something worth ducking into and taking the time to view.