train is easiest way to travel in Italy
Ciao Elisabeth,
Florence is just a short train ride from Rome - most trains that connect the two cities take about an hour and a half. As long as you don't take a "regional" trains that makes lots of stops, you should also be able to return in time to Rome. In any case, I'd make sure to return to Rome and spend the night there before the day of your flight just to not have time constraints. The train from Rome passes through the Tuscan countryside so you'll have a scenic ride.
Once you're in Florence and depending on how much time you have, I recommend also using the train to get to Pisa, Lucca, Arezzo and Siena from Florence. If you have time, you might also want to visit San Gimignano which is a charming medieval village with lots of tower-homes (easily reached via bus from Florence). As long as you aim to visit towns, it is pretty easy to move around with trains and buses and enjoy the Tuscan countryside that way.