Great place to stay. My wife and I stayed for a week with our 3 year old. Only things of note are the restaurant noise and staircase. The restauarants during the week closed early so night was quiet, but friday/saturday were very noisy through 3AM. The staircase was 4 stories so just be prepared for that.
The apartment was very comfortable, a nice couch, chairs, and dining table. The kitchen was great and the clothes washer/dryer were a huge bonus. Only thing I can comment is a microwave would be a nice to have.
San Niccolo itself is definitely where I will recommend anyone to stay. Quick walk to everything Florence with a lot of restaurants and a great grocery store. Very little crowd which is nice after spending a day in the Florence center crowds.