One day trip from port of La Spezia to Florence and Lucca in a day

I don't know if the cruise folks can pre-arrange museum reservations. Traveling from La Spezia to Lucca by train takes at least 1.5 hours with two train changes. From Lucca to Florence it takes also 1.5-2 hours by train (no changes). I doubt you'd be able to see both if you only have half a day. I'd choose only one of the two.

Yes after searched the map I realize by public transportation it will take way too long to get to Florence. It might be the best to book the excursion from La Spezia to Pisa and Florence and back with short stops. Thanks

I think I would just take the train to Florence (2 hrs) and spend the afternoon there. Any cruise ship excursion would be by bus and that would take 3 hrs to Florence and with a stop at Pisa would not leave that much time in Florence - unless you're eager to see Pisa. I'm not sure what time your cruise ship docks but when you know you could get reserved times at either the Uffizi or the Acedamia (Michelangelos' David). Not sure you'd have time for both but you could do one depending on your art interest, then have a nice lunch somewhere and just explore the town - get at least outside views of the Duomo and bell tower, a fountain or two, a church or two, and the Ponte de Vecchio.

Thanks for the advice. I will choose train ride from La Spezia to Florence, and back. Is there a direct train from La Spezia to Florence? Or I have to make a transfer at Pisa? Is there any bus from port to the train station in La Spezia?

You will want to bookmark the Trenitalia website for train times, prices, etc. https://www.trenitalia.com/en.html
Be sure to use the Italian place names : la Spezia Centrale, Firenze SMN. You will most likely need to change trains once.
You can also download the Trenitalia app for tickets, platform numbers, and any time changes. Being so far from the port, don't leave your return too late. You don't want to be a pier runner.

It's a 5 (ish) minute taxi ride between the cruise terminal and the station. A bus will take at least 15 min + wait time. Google Maps can show bus times and routes

You will need to buy timed entry tickets well in advance if you want to visit the Accademia, or Uffizi . You won't have time for both.

Thank you! This is very helpful. My cruise land at 8:30am and will depart at 8:00pm. It looks like train ride is about 2.5hrs each direction, plus waiting time, so it only leaves us 4hrs for the sightseeing. Are the Accademia and Uffizi close to each other? I may just choose one of two as you suggested.

If you are in La Spezia, would highly recommend you take the train to Pisa and spend several hours there. In Pisa there is the Tower, the Baptistry, and the Cathedral. There is also an ancient wall (dating back to 1100s) that you can walk. We also found the Pisa Naval Museum to be very interesting. Thirty minutes south of La Spezia port is Doria Castle which provides great views of the area. Traveling back and forth to Florence in a day from La Spezia will not give you much time to see the sites.