Florence is walkable, but most of what you'll see are other visitors, I'm afraid. It gets very crowded. Giotto's Campanile, the tower next to the cathedral, is worth a climb.Try and get there at opening time - the queues can be ginormous. You can see the whole of the city from the top of the tower. The Ponte alle Grazie is a good place to get the classic shot of the Ponte Vecchio, which its self is worth a visit - lots of colourful people, and not all of them will be after your camera and wallet. Basilica di Santa Croce is where Dante and other famous Italians are interred, and is an amazing building with a terrific plaza. Crossing the river can get you away from the crowds, and a hike up to the Piazzale Michelangelo takes you through some nice stuff, and again gives a great view back over the city. The whole place is incredible, if only they wouldn't let so many bloody tourist in...the food is fantastic!
Enjoy.