I have been to Florence three times. My favorite hotel is Hotel Loggiato dei Serviti . http://www.loggiatodeiservitihotel.it/ It is a converted monestery located in lovely Piazza della Santissima Annunziata, about 10 minutes from the Duomo or 15 minutes or so from the SMN train station. There was a taxi strike when we were there so I can attest from personal experience that it is walkable from SMN!

It's in your price range. Prices start at €120 for the date you plan to go. A superior double room goes for €150. It gets excellent reviews. I've given the hotel web site above for you to explore, but booking might be easier here:
http://en.venere.com/hotels_florence...6,20090517,2,1