From Florence by train to ...

The main station SMN (named after the close by historic church of Santa Maria Novella= SMN) is close to the historic center of Florence. You can park in the underground garage, perhaps more relaxing would be a bus drive to SMN station.
... Rom From SMN trains depart to Rome almost every 30 minutes. The ES (EUROSTAR) will bring you non-stop into down town Rome main station in 1 hour 36 minutes. Rome's main station Termini is located very central; by foot, by subway or one of the many buses you get quickly to all the places you would like to see. Tourist information right at the main station.
... Lucca From SMN almost every hour trains start to Lucca; but be aware, not each of them will bring you there really fast: look for the travelling times indicated, if it says 1 hour 17 minutes you will have found the direct train („direttissimo“). From the nice Lucca train station it is a few steps to the walls (le mura), turn left and enter the historic city through Porta S.Pietro. After some 100 m you will find a bycicle rental (Lucca is the city of bykes „bici“). By foot you will have crossed the city in 30 minutes, a walk around the walls takes roughly one hour, sight seeing underway not counted. Tourist information: circle the walls (on or below them) clock-wise for ¼ and you will get to Piazzale Verdi with info office incorporated into parts of the old fortress. Or you just cross the city and find another Tourist information at Piazza Santa Maria.
...Pisa - Airport Pisa Airport Galileo Galilei can be reached directly by train from Florence. Depending on day time they travel every 2 hours or every 30 minutes. Please check time tables, travel times vary from 1h 20 up to 2 hours.