11 Days in Italy by Train

That's a lot of moving around!
How many nights do you actually have? Count your trip in NIGHTS not DAYS. 2 nights really equals 1.5 days when you account for travel to/from each destination/check in/get oriented, etc.

You've listed day trip to Pompeii twice- is that correct?

We adore Venice just returned from our 2nd visit so I'd want more than a few hours there. If you really are not interested then skip Venice- add the night to Rome and/or Florence- both deserve more time than you have given them.

Have you booked flights already?
Open jaw- fly into Rome and out of elsewhere - usually a better plan so you don't have to double back to Rome the night before your flight home. Maybe check into Rome out of Milan?

We have no interest in CT- the reports of over crowding are a real turn off to us. I'd do day trip out into Tuscany hill towns from Florence instead, but I also think Florence is lovely even if you don't care for museums.

So 2 nights in Rome (recovering from jet lag), 2 nights in Naples, 2 nights in Florence, train to Cinque Terre and then to Venice for 1 night, 3 nights in Bolzano, then train to Rome to catch your flight the same day? You're trying to do waaaaaaaaaaay too much and will spend at least 1/4 of your vacation on a train.

Sorry, the first day trip is Sorrento to Positano. So you suggest cutting out Cinque Terre? I think since we are getting a day trip to Positano we probably don't need to do that. Our flights are booked, we fly out of Toronto on the 25th but don't arrive in Rome until noon on the 26th, and then we leave Rome on the 5th around noon as well. So it is ten nights total. There is just so much to see that we don't want to miss!

And by underrated, I mean overrated! Lol

You are spending so little time in Venice that I don't think it is worth the time and effort (and money) to go there.
There is luggage storage at Pisa Centrale, but not sure of La Spezia. Or will you return to Florence to retrieve your luggage.
Bottom line, it is too much. Assume your airline tickets are bought already. Also Day 12 is the flight home, right?

11th will be the flight home. Would this revised itinerary sound more reasonable?

Arrival/Rome
Rome
Rome
Naples
Naples
Florence
Florence/Venice
Venice/Bolz
Bolzano
Bolzano
Rome/Home

Waaaaay too much moving around. You will be well versed in train seat comparisons, but your trip is a whirlwind with no "down" time and no time to really enjoy your trip or the cities and towns you are visiting. With this number of days, you should consider 2 to 3 places to really enjoy things. Day 7 will be a killer, and you will be like zombies.

You will be back to see all the things you missed. Do the vacation thing rather than the Marathon thing.

So you have 10 nights arriving and departing from Rome.
You simply have too many locations for such a short trip and you are going both north and south.
Pick 3 locations, Do 4 nights, 3 nights, 3 nights.

You will need to be in Rome the night before your departure flight so consider heading immediately on arrival to your first location then put all your Rome nights together at end.

As you have itinerary now you will spend way more time “getting there” than actually “being there”

Going to Venice for a few hours basically guarantees you'll hate the place, because you'll head straight to St. Mark's Square with thousands of your closest friends--which is probably what your "over-rated"-reporting friends did. Don't do that. If you don't have enough time to see some of the less-mobbed parts of Venice, just use the time elsewhere.

Bolzano is a very pretty place, but it is down in the valley, not up in the Dolomites. The usual recommendation is to stay up in the mountains instead. There is bus service from Bolzano, but you'd be making three round-trips if you stayed down in the valley. Otisei is a very popular Dolomite base on this forum. If you do decide to stay in Bolzano, be sure your lodgings are air-conditioned. It can be very hot in Bolzano in the summer, and some of the hoteliers haven't yet bowed to the new reality and installed air conditioning.

The museum housing the Iceman in Bolzano is very good. If you can find a place to store your luggage (might be possible at the Bolzano train station) you could visit the museum on your way to or from the mountains. That would be the most efficient way to handle it if you opt to stay up in the mountains.

Another vote for going to your first non-Roman location immediately upon arrival, and putting all of your Rome nights together at the end of the trip, before departure from Rome. One possibility would be to go to Bolzano upon arrival; it will be a long day's trip, but that first arrival day is often a blur anyway, with jetlag. Then work your way south toward Rome: Florence second, Naples third, Rome last.

Wondering if you have researched your train travel options?
I like to use
www.rome2rio.com
as a starting point just to see what my options are, how long each leg will take.

I think you need to prioritize and pick EITHER south to Naples/Amalfi OR north to Bolzano and head to that location on arrival.
Have you booked any accommodations yet?

Option 1-
Arrive FCO- train to Bolzano- you will have to go to Termini first- 4.5 hour train ride gets you to Bolzano past dinner time. 3 nights there- probably a good place to get over jet lag, although I have not been there.

Train Bolzano to Florence- 3+ hr train ride 3 nights- day trip to CT or Siena or wherever you like but you really have just 2.5 days here in Florence so 1 day trip is all you have time for.

Train Florence to Rome- 1.5 hr train ride 4 nights- arriving early gives you a decent 3 3/4 days in Rome with no jet lag to deal with

Fly home from Rome

Option 2
Arrive FCO- there are direct trains to Florence from FCO (1.5 hr train ride more appealing after a long flight) 3 nights in Florence with 1 day trip

Train from Florence to Naples (or Sorrento?) 3 hr train ride- 3 nights here gives you a half day for Naples, 1 day for Pompeii and Sorrento (doable I suppose- Pompeii was exhausting!) 1 day for a day trip along Amalfi but from Naples this will take longer and definitely a FULL day.

Train from Naples (or Sorrento) to Rome 1+ hr train ride- arriving early and you‘ve got a decent amount of time for Rome- 4 nights.
1 day for Vatican sights, 1 day for Colosseum sights, 1 day for all the rest.
The one museum that is a DO NOT MISS in Rome is the Borghese Gallery- just jaw dropping beauty- all timed entry booked ahead and visits limited to 2 hours so it won't suck up much of your time in Rome

Fly home from Rome

Might as well tell yourselves now that you will be returning to Italy.

None of us knows the length of our days on this earth, but plan to return to Italy -> so you don't feel like you have to cover all of this areas in one trip.

Being young, you probably have WAY more energy, that would aid you :-)

Jet lag is much worse heading home (west) than going there (east). The first two days on the ground are the worst for a mal-adjusted body clock.

Like others have said, I like the idea of getting on a train and heading AWAY from Rome and working your way back.

There is SO much to see / do / eat / walk / experience in any ONE area. You could just go to 3 overall locations.
Review your top picks and see if a fast train will get you between those sites well.

Summer heat and humidity in Rome, Naples, Florence and Venice can be oppressive. Do not underestimate how much that can sap your energy. There's little shade for relief.

It can take 3-4 hours to get from your plane to your hotel. There may be a considerable wait to get through passport control. If you check bags, expect to wait for them. The Leonardo Express takes about 1/2 hour to Rome, runs twice an hour. At the Rome train station (Termini), you still have to find your hotel - either taxi (and maybe a wait there) or public transportation. It's about an 8 hour flight from Toronto. If you're lucky you'll get 5-6 hours sleep. Do not expect to see/do much on Day 1.

Day 3 - Do you want to see the Vatican Museums or just the Sistine Chapel? If only the chapel, look for a private early morning visit. Otherwise go to the church early (7-8 am) before the long security lines, then enter the Vatican Museums with prebooked tickets. Walking quickly through the museums to the Sistine Chapel will take close to an hour. Then you go back to your hotel to get your bags and go to the train station. Figure about 2 hours from hotel Rome to hotel Naples. To save time, stay at a hotel near the Naples train station or at least near a metro station. Otherwise you'll waste a lot of time because of traffic.

Day 4 - There's really not much to see in Sorrento and it's a pain to get there on the local Circumvesuviana train (it's more like a subway than a "real" train). Consider taking a fast train to Salerno, which has well-preserved historic center and a big, sandy beach. Ferries to Positano start there. Or bus from there to Amalfi, then take the other bus to Positano. I'd go one way by bus and the other by ferry. The best thing about the coast is the scenic beauty.

Day 7 - I wouldn't do it. It's 2 to 2.5 hours just on the train to La Spezia. You'll be in the CT with all the other day trippers. Way too crowded. Then it's a minimum train trip of 4.5 hours to Venice.

Day 11 - you wrote that your flight home leaves around noon. You have to be at the airport 2-3 hours before departure! You need to sleep in Rome or you are risking missing your flight. As far as I can tell, it's a minimum train ride of 5-plus hours from Bolzano - more if you stay up in the mountains.