trying to decide what order to visit these cities

Hello ritabtripp, and welcome to the forum!

How long are you planning to be in Italy to see all these places? The number of nights you have for each place is important.

If you want to start in the south then flying into either Naples or Rome is your best bet. Rome to Naples is just over an hour on the fast train and and depending on where you're flying from Rome may be easier to fly into than Naples. Flying out from the north you have the options of Pisa, Florence but the big one is Milan which isn't that close to CT but is much closer than Rome.

Which that decided I would do Naples, Amalfi (via Salerno or Sorrento), Rome and then you would need to define "Tuscany" somewhat.
Siena is reachable by train but much of the famous small rural hilltowns of Tuscany are not well served by public transit. If you are unwilling or uninterested in renting a car and driving it will restrict your options somewhat so this is an important decision.
Cinque Terre and area can all be reached by trains and/or boat so that's pretty straight forward. It sounds like you're going to be visiting CT potentially in early November? You shouldn't plan on swimming and should plan for the possibility of weather.

From there you can train to your destination airport. Use "La Spezia" to check train schedules and timings. Tickets won't be available for November yet but you can check times. Less than an hour to Pisa but 3.5 to 4 hours to Milan. So you're right in trying to figure out which airport is closest.

Hope that helps, have a great trip,
=Tod

That second option sounds like a great idea. If you are going to be visiting the city you fly out of, save that one for last and save your travel times. The trip from Naples (and wherever you might be there) to Cinque Terre will be SO VERY LONG (6-8 hours ish), but the trip to Siena might not be that much less (5-6 hours ish), but ALL of your travels will be long (I just looked and the combinations of location order showed anywhere from 3-6 hours between your destinations). So I would start in Naples/Campania and end in Rome, the other two locations could be probably the same amount of trouble no matter what order they are in. Are you staying particularly in Siena, or did you need to find a place to get a car to start driving through Tuscany? A different location to pick up a car might make it easier.

How much time do you have in total?
Some people just prefer direct flights, so if round trip Rome works best for you, it will work fine. Getting from Rome to Naples is not difficult. I would start south and move north for sure, but I would also consider skipping CT because you can do stunning coastal hikes on the Amalfi Coast and don't necessarily need to do both.

If you want the ideal and don't mind changing flights once, then try all of the options:
Into Naples and out of Pisa, Florence, Rome, or even Genoa

Try to work it where you are in Rome last if you are flying home from there. You could do Naples (AC) - Florence - Rome

I’m doing a somewhat similar trip beginning in a couple of weeks but after Cinque Terra I’m going to Santa Margherita Ligure. I’m flying into Naples and out of Turin. I picked Turing because Turin was a much better deal with Air France miles. But you could fly back from Milan, Genoa, Pisa or Florence or even Turin, but you would need to spend the last night in that city.