Actually, it is not close to the Duomo.
It is on the far eastern edge of the old town, adjacent to the Florence "beltway" - the busy, noisy "Circonvalazione".
It is a long, long walk, and far from the most interesting walk, from the Four Seasons to the center of town.
I assume they will provide a shuttle bus.
Frankly, I cannot imagine staying there. For the same price, you could get a wonderful hotel with wonderful views on the Arno (the Excelsior, the Grand, the Lungarno, for example) or elsewhere in the heart of town (the Savoy, or the Helvetia & Bristol, for example), or you could stay in one of the gorgeous places in the hills (the Villa San Michele, or the Torre di Bellosguardo, for example) and be no further from the center by shuttle.