Docking in Livorno

Walk from Port to Piazza Grande. From Piazza Grande take bus no. 1 to STAZIONE CENTRALE
There are numerous trains to Pisa (about 2 to 5 per hour, depending on time of travel), the cost is €2.60 o/w, the train journey is about 15 min. Then from the Pisa Centrale station you need to take a bus (no. 1 I think) or taxi to the Duomo, because the walk is almost 30 min long.
From Pisa Centrale to Firenze Santa Maria Novella, there are also many trains (2 per hour on average). The train journey ranges from 48 to 83 minutes depending on the train you take. The cost is €8.40 o/w.
Check the train schedule below
www.trenitalia.com
You don't have a whole lot of time. If you want to catch a glimpse of both Pisa and Florence, if I were you I'd go to Florence first and maybe (if you have time) stop in Pisa on the way back. You want to do the farthest place (Florence) first, that way from Pisa you are closer to the ship. If you run out of time you can even take a taxi all the way from Pisa to the port in Livorno (not cheap, at least 40€, but doable)

Excellent advice! Especially about going the greatest distance first in case of lateness on the return. Many thanks!

Livorno Centrale is about 2 miles straight east from the dock, so I suspect you will need a taxi. Trains to Florence (stopping in Pisa) go every hour at 12 past the hour, plus there is an express (1 stop in Pisa) at 8:52.
It takes 1 hour 20 minutes to get to Florence (express 1 hour 8 minutes). Pisa is about 15 minutes from Livorno on the train. Cost is 9.60 euro/P.
Returns are at 28 past the hour and there is an express at 5:00 pm.
These are the current schedules and they may change a tad after June 10.
If you want to visit the Uffizi, get an advance ticket.
I'd say look carefully at what is included in the ship-board offer. If it has scheduled tours of the Uffizi included, might be worth doing even if the price seems steep.
Things being what they are, you might save Pisa for the return to see if you have time. It is a notorious one trick pony. Even though every place matt and pizza box in America has the Leaning Tower printed on it, it just means "This is Italian food".

Thank you, Sam! Great help and appreciate the specific info on trains, etc! I will check out the ship offering in addition to doing it ourselves.

Shirley, if you go on your own, I suggest skipping Pisa & just focusing on Florence. The boat tours, while more costly, will guarantee that you wont be left behind. If you go on your own, make sure to allow a very big time cushion.

Thank you, Bob!