B&B or Hotel in Florence?

I would first write to the hotel and ask them if there is a view of the river from the rooom you have reserved, and go from there. If there IS, I'd say keep it! The location is very close to Ponte Vecchio, the Uffizi, Santa Croce, and the Science Museum (gotta go see Galileo's finger there!). So if you're going to those places anyway, might as well stay put.
I looked it up online and it looks like a really nice place. We stayed in a place that was 75 euro per night, was very small, bathroom across the hall, not super clean, no outside facing windows, packaged "breakfast" items (in-room packaged croissants, etc), and we had to lug our luggage upstairs cuz there was no elevator. It was a few blocks off the Arno, on the other side of the river from your hotel, and we found walking to all points of interest easy and didn't take long at all.

Rebecca....

I can recommend the Soggiorno Battistero right next to the Duomo (some stairs to climb and you will hear the church bells) as well as Residenza Giotto right around the corner (has elevator). We paid less than 100 euros per night back in 2002 for Battistero and about 145 euros in October last year for Giotto. Both are great places and very centrally located for exploring Florence. Giotto has a wonderful terrace with views overlooking the Duomo. Both places included a very basic continental breakfast in their rates.

If I may suggest yet another, we were there in July this year and stayed at the La Residenza Hotel on Via Tornabuoni, which is the street with all of the designer stores. We stayed here for 14 nights at 80 euro a night, had a wonderful breakfast with meat, ham fresh fruit yougert etc. and wonderful service. The location is just great close to everything between the train station and Duomo, so everything is quite close. You might want to check it out, not sure when you are going, but the prices are really good for this area. That was my second trip to Italy and my first time at this hotel, but I am planning already to go back next year and plan to stay here.

I have to second the recommendation for Soggiorno Battistero. We opened the window of our room and looked right out onto the Baptistry and Duomo. Windows were double paned, so noise was not a factor. Couldn't be more centrally located. No breakfast room - they deliver a light continental breakfast to your door.