Florence to Istanbul

Flying is obviously the best option. For non-stop flights, you would have to travel to Rome or Milan and catch your flight there. For flights with 1 or more stops, also look at Florence and Pisa. Last year, Lufthansa had some very good rates to Istanbul. If flying only one way, then using one discount airlines for a flight to Germany and a second for a flight to Istanbul might be a less expensive option.

You didn't say when you were going, but Lufthansa is currently showing one-way flights Florence to Istanbul via Munich, in August, at only $260.10.