A main focus for us, as for all tourists in Italy was the food. And by that I really mean that we ate gelato everyday, had apperitivi regularly and tried to get in as much good pasta and pizza as possible. It was a diet of bread, cheese, ice cream and coffee for the most part. Walking a good 5-6 hours a day made it seem less gluttonous somehow.
One of the walks we took was to a church high above the city. We came across a public garden and some funny art installations. Florence is famous for the Ponte Vecchio, but really all of the bridges can be lovely to look at.