The Traveling Professor has been taking his small group tours to Florence for over 10 years now.  We've seen a variety hotels and here is our choice, selected from Steve Solosky's and Melanie Wilson's new book, The Traveling Professor's Guide to Florence:

Hotel Alessandra. Borgo Santi Apostoli, 17.
Hotel Alessandra is a clean and simple two-star hotel located in a many floor building from 1507.  Most rooms have a front step, and the elevator is only accessible starting on the second floor, making this hotel inaccessible for disabled guests.  Hotel Alessandra has undergone multiple renovations and has soundproof windows which are necessary for its location.  The rooms are versatile, and the hotel can accommodate singles up to family rooms and suites.  Though the decorations are sparse, Hotel Alessandra still offers a nostalgic feeling with antique typewriters in multiple common areas.
Website: www.hotelalessandra.com

Hotel Palazzo Guadagni.  Piazza Santo Spirito, 9.
A lovely place to stay right in Santo Spirito square, this hotel has sixteen rooms, ranging in price, depending on size and view (a couple of superior rooms have gorgeous views of the Duomo).  Like many hotels, it is a converted historical building, with fireplaces and frescos in certain rooms (classic and superior).   There are options for families at Palazzo Guadagni, but it is not handicap accessible.  A small elevator from the ground floor is paired with a few steps up to reception.  Reception is open until around 11:30 pm and a staff member is on call offsite for night emergencies.  Have breakfast in the chandeliered breakfast room or take it to the best part of the hotel: the beautiful porch that looks out over the square and rooftops.  We do not recommend rooms overlooking Santo Spirito for light sleepers.
Website: www.palazzoguadagni.com