If you look for a spacy, well-equiped appartment, close to the historic center (when I say close... I mean less then 200 meters from the Duomo!), look no further!
The Red Pearl Appartment is what you need.
Across the street there is a little supermarket where you can get all food if you plan to cook on the appartment. If not a zillion of streetfood/bars/restaurants are within walking distance (free tip: Osteria Dell'OK ;-)).
Maybe there are two things a visitor needs to know: First, you might have some noise at night, but we didn't care. It's part of the city sound. And secondly, the shower is not the biggest one we've had in the past. But, the water is hot and you come fresh and clean out of it. That's the most important ;-)
We'll recommend this place to everyone who needs a fine stay in Florence.