Travel to Italy 4 cities in 15 days

It would be ideal to fly into Venice and out of Rome, but that would upset all your bookings. With an 11 year old art museums might not be a high priority, I guess. Castel S'Antangelo near the Vatican might be fun though with a child. I always thought that was an underrated sight in Rome. Also, you can rent bikes to ride through the Villa Borghese park, one of the most fun things I did on my last visit to Rome a couple of years ago. The Borghese Gallery might be within the attention span of an 11 year old as well. The Duomo sights in Florence, for sure. Make sure and plan your airport departure carefully, no easy thing making it to Marco Polo for an early departure (one of the reasons why it's better to fly into Venice rather than out of Venice).

I spent a week in LA last July, during the heat wave which you may remember. That's a little closer to Italian summer. While the temps aren't likely to be in the triple digits (like LA was), it will be a lot more humid. Not much in the way of cool breezes, and it doesn't cool off much in the evenings. Do not overplan your days! Your trip seems to be well-paced. Instead of a gondola ride, look into a gondola lesson, cheaper and more fun. After that, you can decide if you also want a gondola ride.

Florence is easy to walk on your own, in my opinion an expensive Segway tour is unnecessary.

Also, you can't go to Florence and miss Michelangelo's David in Accademia! Also, check out the Santa Croce church which is where Galileo, Rossini and Machiavelli are buried.
We love the Hotel Balesteri, on the Arno in Florence.

Since you are traveling light, if you are not opposed to relocating, you might want to add a night to Capri instead of doing a day trip. I think that you will really enjoy everything that the island has to offer then: the Piazetta without the crowds in morning or evening, a boat tour around the island and stops at on the water restaurants, swims in the coves, wonderful easy hikes for an 11 years old, Monte Solaro and it's chair lift, villa san Michele... I spend 5 nights on Capri with my children and loved every moment of it. By spending the night, you won't be competing with all the day trippers and the cruise boat passengers from Naples.

It is a nice, well thought-out plan. For an evening activity in Rome, after the heat has passed, check out http://www.viaggioneifori.it/en/.

I would NOT add another overnight anywhere and make Capri and Pompeii dependent on your energy level. Pompeii should be done as early as possible in the day as it is completely exposed to the sun.

I see you have a segway tour planned. I posted a question about age restrictions a week ago. A lot of tours require a minimum age of 16, my two will be almost 16 when we travel. One reader recommended Rex Tours https://rex-tours.com/en/rome-segway-tour/ancient-rome-2/ does a tour of Rome and requires the riders to be 12. I know you were looking at Florence but this one is in Rome.

A number of people responded negatively toward a segway tour on my post. (Yes, my kids can walk) I have heard nothing but good things about them from people I know and doing one with a teen is a great idea. Contact Rex directly and and you can ask about their age restriction. Plus Rex only requires a 10 Euro down payment for a reservation instead of the entire cost.

I agree with skipping the segway tour and just do a walking tour on your own (put together the sites you are most interested in on a map, or follow one that you'll find in most guidebooks). I take it the full day tour to Siena, San Gimi and PIsa is an organized bus tour. If so, that's fine, not my favorite way to see places by any means, but it is one way to see those three towns in one day. On your own by public transportation it would be almost impossible to do all three in a day. I actually think Siena deserves an entire day, but with your limited time I can see the appeal of getting to see San Gimi and Pisa as well. On the other hand, since you do have three full days in Florence you could consider a one day trip (by bus) to Siena one day and on another day a day trip (by train) to Pisa and Lucca. You wouldn't get to San Gimi, which is a very nice town but will be very crowded for just a few hours mid day which is all you'll get on a tour. How long is the cooking class? Sounds like you'd still have a good deal of "wandering' time that day. I guess it depends on how you prioritize seeing church interiors (with some great art in them) versus exploring the city.

From Sorrento one of your full day trips should certainly be the Amalfi Coast towns - take the boat (I think it's around 9:30 from Sorrento to Amalfi, explore that and then take a bus up to Ravello. Then take the bus to Positano and at the end of the day the bus back to Sorrento. I would go to Pompeii early (get there when it opens). Most people have had enough after 4 or 5 hours so you'd still have a good chunk of the afternoon to explore more of Sorrento.

Thank you everyone for all the tips! Super helpful!