Update: The "new" Florence airport project has been going on for some time now, and the many updates to the airport itself appear to be finished. There is a brand new check in hall, and other improvements and enlargements are also planned to come online in 2013.
The Florence Airport (FLR) is named "Amerigo Vespucci Airport" but is also known by many people by its old name "Peretola" (many road signs still have this name on it, more history of Peretola here), which is the area where the airport is located. The airport is about 5 kilometers from the city center. There is now a fixed taxi fare of € 20 (nights, Sundays, and baggage are extra) from the airport to the center. There is also a bus shuttle run by ATAF from the airport to the main train station (Firenze, Santa Maria Novella) every half hour from early morning to 8:00 PM.
This is a small airport, with one runway (which was recently expanded to handle larger planes) - there is a larger one at Pisa, Galileo Galilei, which is 80 kilometers away. Florence Airport has a bar/café, a duty free shop, and a currency exchange. The airport handles about 2 million passengers a year.
Amerigo Vespucci Airport
Via del Termine 11
Information on flights (24 hours): 39 055 3061700 Ext. 702