If you are English speaking and need a doctor in Florence, even if you need an emergency house call (! remember those?) - Medical Service Firenze is a great choice. Over the years, even though we have been covered by the Italian health care system most of the time, we have used their services in between coverage gaps or during emergencies, etc.
Office visits are very reasonably priced, the doctors all speak English, and you can just walk in during their posted open hours. And the office is right in the center of Florence, on Via Roma just down the street from Piazza Repubblica heading towards the Baptistry (basically across the street from LUISAVIAROMA).