First and foremost the Duomo. Another day, another duomo. We opted to hike up the tower for the views of the city.
'Ino. It was hands-down the best sandwiches we tried in Italy - a cool spot close to the Ponte Vecchio - put it on your short list.
Gelateria della Passera - I would rank this as the second best gelato we had on the trip...and it is right on this small plaza with a coffee shop and restaurant - I promise you it will be worth the effort to scout it out and find it!
Da Delfina early on in the planning stages. The setting is gorgeous - in the middle of Tuscan vineyards and hills - we loved it. And, the food was great. If you are in the area, we would highly recommend it for dinner.
Hotel Continentale literally right next to the Ponte Vecchio.