Unfortunately, I'm not a really big fan of art.
First half an hour: 'wow cool' ( stood one minute and observe)
Next hour: 'err. . did I see this painting before somewhere?'
Remaining hours: 'I guess we've seen enough art for the week'
One of the most interesting section there was for Leonardo Da Vinci's works.
Another interesting place in Florence is the Old Bridge ( Ponte Vecchio). A short bridge with houses built on top ( mostly shops) and one of the main tourist attraction.