Italy and Greece in 3 weeks with teen

2 nights traveling toward Cinque Terre, seeing high lights Florence, Naples, Pisa ?

Naples is SOUTH of Rome; Pisa, Florence & CT are North.

By late June all your destinations will be filled with folk like you, ( i.e. tourists.) so how much "of a relaxing and cultural trip" it will be is uncertain. Just be prepared to have lots of other tourist folk around.

Yeah that 2 nights between Rome and CT needs some work, but looks doable otherwise. See if there are any flights to Santorini from Genoa or Pisa--might save you some time. (Note they could be seasonal flights)
When/where are the classes? You only have two full days in Rome, so that could be tight.
If your daughter does not like hiking, be sure to plan some activities for CT.

Welcome!

How many nights do you actually have for this trip not counting your overnight flight to Europe?

If you fly from Rome to Santorini you will probably need to stay in Rome the night before

Could consider traveling onward to Florence once you land at FCO the put your Rome nights all together mid trip

Something like
Land in Rome
Florence 2 nights
CT 3 nights
Rome 3-4 nights
Then on to Greece

You can stop in Pisa on your way to or from CT
Naples is obviously the wrong direction
Expect large crowds everywhere
Book CT as early as you can

Thank you for the responses! We do not have anything booked yet, trying to figure out a rough itinerary and we are very flexible. We understand this will be high tourist season, but summer is our only option with school.
We would like to fly out on June 13th and return home on July 3/4.
We are also considering just doing Greece, but really liked the idea of seeing a little of Italy, plus I read Italy is more affordable and easier to get around?

I love the idea of either moving Rome to the end of the Italy portion prior to flying to Greece or fly to Santorini from Florence, those
flights were similar in price and time.

For the 2 nights to CT, I mixed up Naples and Siena, I have been researching so much everything is running together at this point. We are considering Siena, Pisa, a day in Florence just to get a sense, maybe Orvieto.

My daughter and I loved Florence. I hope you can go!

pbscd, What were your daughter's favorite things in Florence?

Uffizi Gallery, definitely! But she loves art. We went to the Accademia that morning (it was amazing) with our tour group, and the guide mentioned something about the Birth of Venus by Botticelli, which is at Uffizi, and the guide said it was about a 20 minute walk from the Accademia. But I also wanted to see Galileo's and Michaelangelo's graves at Santa Croce, so we stopped there on our way, I do recommend it, and then had about 2 hours at the Uffizi. I was so exhausted but I'm really glad we went, and she was grateful. It ended up being a highlight of our entire 13 day tour. She stood by the Birth of Venus painting a good 20 minutes just studying it. I was hoping she was enjoying it (she's not a super demonstrative person) but she was loving it. Then in the room next door, was his Spring, and of course that needed some time to study. But it was amazing seeing so many paintings in person that we've only ever seen prints of! Now we're planning a trip to Paris, primarily to see the Louvre and 7 other art museums. It was all wonderful, truly, and I'm so glad we could experience it. Florence is very very walkable. I actually heard recently on a podcast that Florence produced such a great number of thinkers and artists and this may have been in part, due to the thinking time they were provided while walking.

Edit: she was 14 at the time of our trip.