We are just winding up our Florence, Venice, Rome trip. I am traveling with my 13 year old who is not a fan of crowds or art museums so that has colored our trip. But I thought I would mention a few things that we enjoyed.
In Florence we hired a private driver to go to Lucca and Tellaro. This was a major splurge (400 euros) but it was a delightful day. We rented bikes in Lucca and rode on top of the wall (this was inexpensive). We also climbed the Torre Guinigi, which has trees growing out of the top. My son particularly liked this because you could climb all the way to the top. (He also liked climbing the leaning tower of Pisa, but there is another level you cannot climb, which disappoint him slightly). We ate at Il Delfino in Tellaro and the service was lovely and the food was wonderful. I chose Tellaro because I kept reading about how crowded Cinque Terre can be during the summer and I wanted to see a fishing village. This took most of a day. The time in Lucca was probably two to two and a half hours.
We liked Venice a lot. We both enjoyed Murano. I liked Burano, but my son was a little over it by the time we got there. We could have done both in about three and a half to four hours, but we also had lunch on Mazzorabo (island adjacent to Burano.). FYI, We both got a lot of mosquito bites in Venice, despite having an air conditioned room.
In Rome, I booked a Colosseum after dark tour through city wonders. It covered more than just the Colosseum, but ended there. Because of the time of year, it was not actually dark, but the Colosseum had only a few tour groups in it and felt nearly empty. (Also it had cooled off enough that we were not sweating through the whole thing.). I felt this was very worthwhile. It took two and a half hours.
We also had a city wonders tour to Ostia Antica via train. For us, this was worthwhile as it would have taken a lot of research and planning for me to be able to understand (and convey to my kid) what we were looking at. The site was huge, uncrowded, and very interesting to me (somewhat interesting to my kid.). We went on a Sunday and the train to the site was extremely crowded due to people going to the beach--one stop further. So I would suggest a weekday if you are traveling during beach weather. This took a bit more than half a day.
I also booked breakfast at the Vatican through the official website. The food was meh. We did get to the
Sistine Chapel well ahead of the crowds which was very worthwhile, IMO. The line to get into the museum when we came out was appalling. I think some sort of skip the line/early access is Important though I'm not sure I'd do the breakfast again. And fwiw, there seemed to be some preference for outside tour groups.
I hope you have a wonderful trip.