Here are two of The Traveling Professor's picks for hotels in the Oltrarno area of Florence:

Hotel Palazzo Guadagni.  Piazza Santo Spirito, 9, Moderate.
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 is paired with a few steps up to reception.  Reception is open until around 11:30pm, 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.  Rooms overlooking Santo Spirito are not recommended for light sleepers.
Website: www.palazzoguadagni.com

Palazzo Belfiore. Via dei Velluti, 8. Moderate.
For those travelers who are interested in staying in the comforts of an apartment instead of a typical hotel, Palazzo Belfiore is the right fit.  With multiple apartment sizes to accommodate different needs (the ground floor apartment is handicap accessible), the family targeted spaces are equipped with small kitchens and comforts for long stays.  Palazzo Belfiore attracts many international guests, and has been successful even as a young business.  The apartments’ management has found a way to connect with guests even without a reception desk.  They book private tours for guests and have an “in room gift shop” inclusive of local artisan gifts.  Contact Palazzo Belfiore directly by website or phone to receive a discount for not booking through an agency.
Website: www.palazzobelfiore.it 

These selections are courtesy of Melanie Wilson who will co-author the upcoming Traveling Professor's Guide to Florence, available Spring 2019 on Amazon.com