Hello briargatebeagles1, and welcome to the forum,
You don't mention a month but I have to agree with most people here that it is not the best day trip from Florence. Not only because of the logistics but because everyone will be doing the same thing. I travelled from Lucca to Pietrasanta which shares a short section of the train line with this trip and the train was packed in September with people heading to CT.
I stayed in PV for several days a few years ago and my pictures will make you want to go but I found it just generally overrun but tour groups because the CT ferry stops there and the tiny town is just packed with daytrippers. If you want to go to the area I found the south coast of the bay San Terezno, Lerici, Tellaro and even Sarzana over the hill much more interesting. The local train may stop in Sarzana just before La Spezia and the other towns will need to connected by bus which is why I think it's all Italian tourists at the seaside and not Americans.
If you are not beach people there are many better IMHO day trips from Florence:
Top recommendation is always Siena - easily accessible by bus and train. Bus drops you more in town so if you take the train consider a taxi to minimize the walking to and from the train station. A good cathedral, a city to explore and one of Italy's great piazzas.
Arezzo is another ancient town (Etruscan roots) and while not as scenic as Siena it is also less touristy and is easily accessible by train. An interesting blend of modern Italy on the flat by the train station blending slowly into the ancient flowing uphill.
Bologna is 30 minutes by fast train and while another large city very different than Florence. Long colonnaded streets, interesting archaeological museum, and great markets as it considered to the food center of Italy.
Lucca is a small medieval town surrounded by walkable walls and is flat. Some interesting churches, music centric activities and some shopping. There are a couple of wanderable palazzos in Lucca - most notably Museo Nazionale di Palazzo Mansi which is interesting but not a blockbuster. Reachable by train - easy but about 1:15 on the slow train. Can be paired with Pisa for a long day.
Verona is 1:30 on the fast train and an outlier but the center is completely flat, pedestrian, great shopping district, Roman gates. an intact Roman arena and theater (still in use) archaeological museum. Although the museum is sprawling above the theater and requires a fair amount of up and down. It has a very strolling, cafe culture vibe. Take a bus or a taxi 8 minutes to Piazza Bra from the station.
Have a great trip,
=Tod