We enjoyed staying at Leonardo House. It's a hostel rather than a private house but having Leonardo on the front desk being friendly and helpful really helped to make the stay enjoyable and easy for a first-timer to Florence. It's super central, midway between the station and the Duomo, an easy walk to both. The room was quiet in terms of street noise, but unfortunately we could hear bathroom noises from the shared bathroom pretty well. I definitely recommend this place if want something reasonably priced and in a handy location.