score:16
Here are a few possibilities:
Milan Malpensa. This a major hub, served from everywhere but there is no longer a direct Frecciarossa to Firenze. (Nor any other train as far as I am aware) so it takes 2:46 and a connection in Milano Centrale.
Rome Fiumicino. Even bigger selection, there are two direct frecciargento trains per day so catching one of them takes a little less than 2.5 hours.
Bologna Guglielmo Marconi. Many more destinations than Firenze but no transoceanic flights, there's a Dubai flight. There is no direct train but there's a direct bus which only takes 1:25. If you try to get to the bus stop from say the Stazione Galeria Ataf stop (ie the main entrance of the station where a billion Ataf buses stop) you need to walk the length of the train station inside along track 16, it's near impossible to cross Viale Filippo Strozzi if you are walking down Via Valfonda, there's a nice covered walking bridge and a ramp down the opposite side but there are no stairs going up on the station side from the street! Check Google Maps:
View from the street:
Also they are building the Marconi Express which will connect the airport with Bologna Centrale Station in 2019.