Freddie.. taxi service to Florence from Livorno would not come cheaply.. If you booked a "tour guide" to drive you around for the day, you probably are looking at $300 to $400...
We took the train, went to Florence first and stopped at Pisa on the way back to Livorno. The only thing of interest is the tower in Pisa, so if you do it in this order you can determine if you have enough time after seeing Florence. You will have to pick and choose a couple of major things to see in Florence and there is no way to do the whole place justice in 1 day.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013