The next morning we got up really early (to Pip's disgust) to see the Duomo in lovely early morning Tuscan light, without the crowds. The building itself is not open till later, but we walked all round it taking photos.
The hotel we found was the Hotel Scoti, in a very central position and good value (by Florentine standards). It is on the second floor of a palazzo, and the lounge contains a wonderful, newly restored set of frescos. The owner is an Australian-Italian and good English is spoken. (This was an unanticipated but welcome advantage.) Contact via www.hotelscoti.com.