Direct ferry routes exist to Barcelona,Bastia,Golfo Aranci,Olbia,Palermo andPorto Vechio. It is best to book early to avoid over booking.
Many cruise ships stop here for at least a full day to allow guests to tour Florence and/or Pisa. Guests not taking cruise ship arranged tours can take a shuttle supplied by the port to the the downtown area. It offers a decent shopping experience, but not compared to Florence. A further 10-20 minute walk or another bus ride gets you to a train station. There you can take frequent departures for either Pisa or Florence. Many experts advise seeing Florence or Pisa on a one-day port visit by cruise ship. Though some tours claim to cover both, you'll get no more than a rushed look at a few icons...and if you're too early or late for any, it may well be closed.
If hoping for maximum time in Florence...
Take an early cab perhaps shared with another couple from your ship to and from the Livorno train station.
At the station, ask for a train that goes to the Firenze Santa Maria Novella. Locals will happily help.