Most of these locations can be timed as getting from Florence to La Spezia and then the time from there onto to your destination, Unfortunately looking in May all the best train times seem to be 2-2:30 to La Spezia and any travel onward from there adds more time so you're committing to a long day of travel (4+ hours certainly) if you want to day trip.
The closest is Porto Venere which is a train to La Spezia and then some sort of transportation - bus, taxi, ferry - to PV proper. For this trouble I would actually suggest checking out the southern side of the day instead - San Terenzo, Lerici and maybe Tellaro.
For Porto Fino check the train schedule to Santa Margherita Ligure but this is another hour past La Spezia. All along that section of coast there are many towns to explore Rapallo, Chiavari, Sestri Levante and many more but I don't know how much time you'll have with the long travel time in the day already.
Hope that helps, have a great trip,
=Tod