La Spezia to Florence

Take the train.
https://www.thetrainline.com/?redirected=true

You can also take an excursion with the cruise line. I have heard horror stories of traffic issues getting back from Florence to the cruise port. Of course that may not be an issue if you take the train. We ran into significant traffic last year getting back from Pisa to the cruise port although we were at Livorno, not Le Spezia.

Because Florence is 2-3 hours from La Spezia one-way by train, I'd sign up for the cruise excursion, so that I know I'd get back in time. If you have a group of people, you might ask the tourist information desk in the cruise terminal to order you a minivan, but expect to pay at least €100 per person for a day trip, and probably more. For La Spezia, Pisa or Lucca is possible to do on your own via the train, but Florence is really too far.

The fastest train is just under two hours each way. I doubt a van would be faster.

mary,

The fastest trip I could find was 1H:45M from La Spezia Centrale to Firenze S.M. Novella (one change at Pisa Centrale). In addition to that, you'd have to add the time getting off the ship and to and from the station in La Spezia. One of the trains is a Regionale, so DON'T forget to validate the ticket prior to boarding the train, or you'll be subject to hefty fines which will be collected on the spot.

While it's unlikely, there's always the chance that the trains could be delayed for some reason on the return trip. For that reason, I tend to agree with T in that it might be better to use the excursion offered by the cruise ship.

You might get some insight into which option to choose by having a look at the Rick Steves Mediterranean Cruise Ports guidebook. You should be able to find a copy at your local library.