Our family will be in Cinque Terre and our first thought was to go to Florence by train, but now we are thinking of renting a car in La Spezia just south of Cinque Terre so we can see Lucca and Colloidi on our way to Florence . Spend 5 days in Tuscany and bring car back to Florence. Some say you should bring car back to same location to avoid problems. Anyone have experience with this?
There's no need to bring the car back to the same location within one country, as long as you choose a vendor with offices in both cities. Avis, Budget, Europcar, and Hertz are the majors located in La Spezia. AutoEurope.com may work with all of these and help you to compare rates.
You do not want a car in Florence.
Since you have to take the train out of Cinque Terre, why not train to Lucca and check your baggage, see the town, and continue to Florence. Unless you have a particular desire, based on what we saw, Collodi might be a disappointment. Bag check service at Lucca: https://www.touristcenterlucca.com/servizi_dettagli.php?quale=2
You can also rent from Avis and Europcar in Lucca.
If you go with the rental from La Spezia (or Lucca), mind the rental office hours, no Sat. pm or Sunday or Lunch time. Avis/Budget is the easiest as you can walk from the La Spezia train station, but that Avis also closes for Sat. am.
Read this about driving in Italy and restrictions involved [ZTLs]; never leave anything of value in a vehicle when parked:
A car is most useful out in the countryside, towns and villages not easily served by public transportation. For towns/cities served by buses/trains a car is a liability.
Thanks for all your help that helped so much