Tuscany

Welcome!

Assuming you will have a car?

Here is info on Tuscany- which is a very large region

https://www.ricksteves.com/europe/italy/tuscany

You should be IN Rome the night before your flight

It sounds like you have two nights between CT and Rome to spend somewhere in Tuscany.
14th Leaving CT - Tuscany (part day)
15th Tuscany (full day)
16th Leave Tuscany for Rome (maybe partial day) for airport the next morning

If you have a car it's probably about at least 4 hour drive from La Spezia once your out of the CT proper to get there.

If you are not planning on having a car then rural Tuscany can be difficult to visit - especially out of the way places like Saturnia. If it's the baths you're interested in there are probably more accessible places you can visit. Using the train places like Siena, Pisa, Lucca and Arezzo are popular Tuscan destinations.

If you clarify your circumstances and interests I'm sure people will offer more suggestions.

=Tod