I would recommend looking at www.florenceby.com which allows you to search by neighborhood as well as star-rating. This company has websites for several cities.

In Florence, I would consider staying in the Oltrarno area (across the Arno), near the Pitti Palace, which is also a close walk across the Ponte Vecchio to the Uffizi. It is much quieter, safe, and has some great hotels like Pensione Annalena, which we loved: www.hotelannalena.it

DON'T MISS The Pitti Palace and its Palatine Gallery to see how the Medicis lived...you will be repeatedly picking your jaw up off the floor!
http://www.inflorencetoday.com/museums/pittipalace.htm