If you're going to Florence looking for Posche-oriented things to do, well, you've already missed the entire point of going to Italy in the first place.
Florence is spectactular for it's history. And the shopping. World class.
And of course, the food, the food, the food. Four courses for lunch. Five courses for dinner. Make every meal truly an event. Ask for the tasting menus. The Maitre'D and Waiter will instantly become your friends.
Oh. Take a day trip to the walled city of Lucca. Wonderful.
Have fun!
