Italy Itinerary

Trains are very easy to navigate in Italy. Don't bother purchasing a rail pass. If you know what time you want to head to the next city, you can purchase train tickets a few months ahead for some great discounts. Otherwise, just purchase your tickets as you go.

Jean has given you good advice on trains. I would only add that once your itinerary is set in stone, purchase your high-speed links in advance on CaptainTrain.com. You'll save a lot of Euros.

Your order of travel is good. What time of year is this trip? That could influence some advice.

I feel like your Florence and Sorrento times are rushed, but doable. Have you considered more time in Tuscany, i.e., make Florence your base for 5 nights and skip Sorrento? You can use Florence to see Chianti (take a tour with Tours By Roberto) and Siena, at a minimum.

Personally, I am not a fan of Capri. It is pretty but very expensive and I felt after our time there that we could have spent it better. Pompeii, however, is very worth the time but I cannot imagine being there in the height of summer. That's why it would be good to know when you are traveling.

Day 11 - You might find Positano a more spectacular choice for the day.
Pompeii and Naples might be worth a few hours each on your way to and from Sorrento - just store your bags.
I would like an extra night in Florence, but it would probably have to come from Cinque Terre.

I also feel you aren't spending enough time in Florence and Tuscany.

Although you say Pisa is a priority, I would suggest hitting it as early in the morning as possible. I found Pisa to be really one-dimensional (the bell tower) and over-run by hoards of tourists wielding selfie sticks (like swords) and/or trying to get the perfect "holding up the tower" shot.

Lucca, just down the rail line from Pisa, is a much more charming medieval city. You might consider going directly to Florence and doing Pisa (or Pisa AND Lucca) as a day trip from there.

Plan looks good to me.
You will be in Florence but really not seeing Tuscany which I think other posters are alluding to but nothing really wrong with that. You would have to add days or remove something else I think to see both so like most trips have to compromise somewhere.

On the Sorrento portion:
If you need to get back to Rome for flying out, might as well bypass it first and stay there last as you have planned.
Only way to make that better is to go to Rome first and then fly out of Naples after Sorrento. That may mean a connecting flight rather than direct or more airfare cost, something you should look into though.
I do think the day trip to Capri is a great idea and would not change that, what I would change is the Day 11 I would on this day take the SITA bus and explore the Amalfi Coast road and towns of Positano, Amalfi and Ravello this day.
If that is not of interest Pompeii this day I would also prefer over a day in Sorrento
You won't be able to see everything of course given the time in each place and need to hope for good weather since you don't have much downtime but looks like a solid plan.

You are spending 5-6 days getting from place to place. that is a third of your trip. Extend the time in some of the places and reduce your travel days to 3-4 and leave something to come back to. The risk is wanting to see it all and what happens is that you spend a lot of time in a train/plane/car and not experiencing the cities you are trying to see. Enjoy your time.

Thanks so much everyone for your input. My friend wants to see Pisa and so we'll keep that one on there, I was just interested Sorrento because Rick Steves said use that as a base for visiting the Amalfi Coast which I would love to do. Perhaps we may cut Capri out to save a day of traveling? I wouldn't be against cutting a day from Cinque Terre to give to Florence.

We're going in August and so I know that wil be a busy busy time. Is there anything that I might change with us going at that time?

Ahhh, August! Heat, heat and more heat! In the Cinque Terre, research some hikes away fro Trail #2. Get out EARLY, take the pausa in the afternoon, and re-emerge when the day trippers are gone.