If you'd really like to see both Pisa & Florence in a day, and money's not an issue, the easiest way to do it would be by taking one of the private tours as AF1 suggested above. It would maximize your time, that's for sure.
If you like to play it safe and want to stay close to your fellow cruisers, "Florence and Pisa On your Own tour" is the way to go.
Honestly, there is nothing much to see in Pisa apart from the leaning tower so the tour will give you a chance to spend some 20 min around the Field of Miracles, take the famous shot and that's it! And as I said, there's no point spending more time there anyway.
After visiting Pisa, the tour will proceed to Florence and give you about 4 hours there.
On the other hand, taking a train is much cheaper!
You asked how to get from Livorno to Florence so here it goes, some instructions on how to get there on your own, by train...
Not sure which cruise line you'll be with but last season one of them (RCI) had an option of booking a special transfer bus straight from the ship to the train station as opposed to the port bus that takes you to Livorno Piazza Grande.
This bus wasn't advertised AT ALL and it was only for those who specifically inquired about it at the Shore Excursions desk. However, this season this might not be the case and you won't know until you get to the ship (and as I said it all depends on the cruise line and their tour operator).
If that doesn't work out, you can always take the regular port bus to Livorno Piazza Grande which all cruise lines organize.
As most people go on organized tours, those do not depart very frequently early in the morning, and they always wait for the bus to be full.
So it can easily happen you'll be sitting on that bus for 20-30 min before it actually departs.
For those in the rush to get to the train station at the time THEY have in mind...oh, well, they might be in for some stress.
Especially those who have their times set to enter the Academia or Uffizzi!
Keep in mind that regardless of the fact that your ship might dock in Livorno at 7am, you probably won't catch earlier train than 9:10 am!
So, be on that bus AT LEAST one hour before your train to Florence/Pisa leaves.
Even so, always make sure you get off that bus first, buy your local bus tickets in the tobacco first, be at the train station counter first...I'm not joking, use your elbows, beat the crowds!
Trains to Florence go only once an hour and sometimes seconds decide whether you'll be on that train. If not, you might be wasting an hour of precious time.
So here's the procedure:
- Get off at Livorno Piazza Grande
- Rush to the tobacco across the street and buy your local bus ticket here (not the train ticket, they'll rip you off).
- at the square, cross the street in front of Mc Donalds, wait for bus 1 or 1A.
- rush off the bus straight to the ticket counter at the train station, be the first in line!
- validate your ticket in the yellow box on the way to the train
- get on the train...relax!
You'll be in Pisa in about 20 minutes. If you decide to get off and go to the tower, always check when your next train to Florence is. Try to do this whole Pisa thing in about an hour or you will waste too much time!
If you do Pisa, keep in mind you probably won't be in Florence earlier than noon!
Catch the local bus to the tower just across the street from the train station, I think it's numer 1 or 1A, too. Not sure, you will see other tourist doing it, too. Note: be aware of the pickpockets on the bus! They come "in form" of cute little teenage girls!
Once you get to Florence, buy your tickets to go back straight away!
Later on in the afternoon the line can be way too long and you risk to miss your train and your ship! I think the latest train to take to be sure you won't miss your ship is the one that departs around 3:30!
So, that would give you about 3 hours in Florence. Not much really...but then again enough to see the Cathedral, Santa Crocce and the Ponte Vecchio and have a quick cappuccino.
Allow more than an hour to return from the train station in Livorno to the cruise ship if you're gonna be using the local bus/cruise line bus.
Make sure you inquire with your cruise line what time the last bus is from Piaza Grande Livorno to the ship! Sometimes it's actually one hour before departure or all aboard time! If you'll be taking a taxi (normally 15-20 euros) to the ship, you can allow less time (30 min) before all aboard time.
If you decide to do both on your own in a day, it could be stressful. So, if i had to chose between Florence and Pisa, I would ALWAYS go for Florence!
Taking a taxi to the train station - most taxis that are allowed to be parked right in front of the ship want to take you for a whole day tour and won't be willing to take you to the train station. However, if you walk only 50 m towards the dock exit, you might find local taxis that will take you to the train station.
Walking to through the dock area is absolutely not allowed and it would take you hm...an hour or more to the train station anyway!
Hope this helps! Have a great day in Florence!