Although it was almost 10 years ago (eek!) that I studied abroad in Florence, Italy with API, I still have fond and positive memories of my time there. They were extremely accommodating and helpful as at that time I was the only student doing the year long program. I lived in two different apartments each semester and they did a fantastic job with matching me with compatible roommates. I am still in touch with some of them today! My apartment during the second semester was steps from the Duomo.. absolutely incredible!
For future participants I would highly suggest using API. I would only remind you that Florence is extremely touristy and one of the more popular study abroad destinations. Perfect, if this is your first long term trip as I'm sure you'll make lots of new friends from your home country and even find American style restaurants. If you want a more cultural and authentic experience I would suggest trying a different city, but continue with API!