We did something similar this past summer (late July/early August) with our then 12 and 15 year olds! After a 8-night Croatia/Greece cruise, we stayed in Venice for 2 nights, Florence for 2 and Rome for 4.
We stayed in Airbnbs in both Venice and Florence which was great because it gave us a little more room and the kids really needed some of that downtime (with wifi!) in the evenings and mornings. Both of them were pretty close to the train stations - that was a MUST for me since we'd be hauling our luggage around.
We stayed in a lovely Airbnb in Venice that was on a very quiet street, but could be along the Grand Canal in 2 minutes. It was a 25 minute or so walk to St. Marks, but part of the fun was meandering there and taking in the sights and the food and shops on the way. We did a gondola ride - and got in during the early evening just before the rates went up 20 euro!
We had a private guide in Florence for a walking tour through toursbylocals.com - she was excellent - would highly recommend! The kids also really enjoyed going to the Mercato Centrale for dinner one night - there were all sorts of stations and they liked picking out exactly what they wanted in a less formal environment.
In Rome, we did a few tours with Walks of Italy - all of them were great. We did "Pristine Sistine" which my husband and I thought was fantastic. It was pretty early for the kids, and maybe not the MOST interesting for them, but after years of Catholic grade school for each of them, we thought it was important for them!
We did the Walks Pasta Making class one evening and it was definitely a highlight of the trip!! The kids LOVED it and we've made pasta as a family at home since. We also did the Pompeii/Positano day trip - which was a very long day (13 hours) and lots of time in the mini bus, but the bus was comfortable and it was worth it to see those 2 places. Pompeii was my 12 year old son's favorite thing of the whole trip - he loved that it was not just "restored old stuff like it would have been" but the ACTUAL buildings! The final Walks tour we did was the Collosseum/Roman Forum tour which was very interesting.
The whole trip was fantastic - we loved trying as many possible gelato places to determine our favorites (didn't find a great one in Venice, Strego Nocciola in Florence and Gelateria S.M.Maggiore in Rome!) My son has sighed wistfully a few times in the past months and said "I really miss Europe - some day I want to take my family there" so we know that trip was all worth it!
If you want more details on our itinerary/trains/Airbnbs/etc - just send me a DM and I'd be glad to share!