The distances in Europe are very short. What you can do here you can hardly do in America or Asia where between point and point are sometimes hundreds or thousands of kilometers away.
Florence is one of the most touristic cities in Italy. She is beautiful, I love her. I spent five great days in it, walking, walking, walking. The good thing is that it has an international airport, small, yes, but an airport nonetheless. If you don't want to go back to Rome or move to Milan, you can use the Peretola International Airport, Florence, which connects with many cities in Europe. Also, getting from the center of Florence to the airport is super easy.
Florence is a small city so you can easily walk to the Santa Maria Novella station, the heart of transport in the city. If you have heavy luggage there are also taxis, of course, but sometimes the distance is so short that it is not worth it. You see older people using the taxis, that's for sure. There is a bus that runs between Florence and the airport: the Volainbus.
El Volain bus It has the stop in front of the Florence train station, on one of the side streets, the one that overlooks the church. It departs every half hour and runs between 6 am and 11:30 pm. You can buy the ticket above the bus (one way, the round trip is for residents), or at the station itself in advance. The bad thing is that there is no stop with a roof so if it rains or the sun is strong it is uncomfortable. Afterwards, the trip is done in half an hour with traffic and less if it is a quiet day.