Florence is on the main Italian high-speed rail corridor: Rome is 1 hour 20 minutes on the Frecciarossa (trains every 30 minutes), Milan is 1 hour 45 minutes, Venice 2 hours. Florence Santa Maria Novella station is in the centre of the city; there's also Firenze Campo di Marte station for some services.
Amerigo Vespucci Airport (FLR) is 4 km from the city centre — much closer than Rome or Milan airports — with direct connections to most European hubs. A fast tram (T2) connects airport to city centre in 20 minutes. From Bologna by road is 100 km; from Rome 275 km.
For routes from northern Europe, the overnight Nightjet train from Vienna and Paris is bookable and saves a hotel night.