Hi, sportel, I saw this when you posted but was actually in Venice at the time so had to wait to get back to answer you!
The on-your-own time is scattered on this trip - an afternoon here, an evening there, and is subject to change, so I wouldn't set any plans in stone. We bought tix to the Uffizi ahead of time because we were sure we wanted to do that in Florence, and then it turned out that the guides had arranged as a surprise to take anyone who wanted to go one evening. (We were there at Christmas time, so were staying in the city not out in the country, so this particular example might not apply to you, but you get the idea.)
Having said that, I can tell you some "pop-in" things we did on our own that were great and that you don't need to plan too far ahead for. We are big into history and art, so not sure you will like it all, but fwiw, here's what we liked:
In Rome, we did the Museum and Crypt of the Capuchins, and it was really cool. Other than that we mostly walked and looked. Such an amazing city! Not sure how old your kids are, but if they're old enough to get into photography, this is the city to get started with it. So many statues, building flourishes, and scenic views to record! You could even set up a themed "scavenger hunt" and take photos of arches, winged people, fancy animal water spouts, or whatever your kids get excited about.
In Florence, Palazzo Vechhio is amazing, especially if you're a Dan Brown fan, but also just if you like incredible historical buildings. There is the palace to tour and a tower to climb. Of course, the Uffizi is a big draw, although I will say it was a little overwhelming. Rick Steves does a good audio tour podcast of it, which makes it a little more manageable and gets you to the highlights.
Also in Florence, there is a really cool medieval house museum called Palazzo Davanzati that is basically a preserved home from the 1300s. The wall painting alone is worth the entry. This wasn't on our radar at all, but we sat up front in the van that took us to our
ABD dinner one night, and got to chatting with the driver and he told us about it. You can see the whole thing in an hour, and it gave me a real vision of how people lived at the time. Since then, DD has started studying art history at college, and one day this Palazzo came up in her Renaissance class. So it's actually a big deal, apparently.
Other things people do in Florence is climb the tower by the Duomo and tour the Duomo. (Can you tell we had more time in Florence on our own than in Rome?)
In Venice, if you like art and/or old churches, you can easily fill a day just walking and stopping in to any church that is open. I would especially suggest you find your way to Campo dei Frari and tour both the Frari church and the nearby Scoula de San Rocco. (Finding your way is easy, there will be yellow signs pointing you toward both of these as you walk along. It is very close to where you will do the mask painting, and we were given free time right after that.) The Frari contains Titian's Assumption, in place as it was originally intended to be viewed, a rare thing for this type of work. The Scoula, especially the upstairs portion, is pretty impressive as well. If you need more art, the Ca d'Oro is full of incredible pieces in a wonderful Venetian palace setting. If you need more active stuff, you can climb the Campanile in St. Mark's square.
As for meals, we've found on our ABDs that if we get too fixated on a particular restaurant ahead of time, it always turns out to be a little inconvenient or to add stress trying to get to it. You are turned loose at different points and places each day, and who knows when you will be hungry or not? We've found it better to rely on our guides to make reservations for us at good dinner spots, and for the lunch on our own time, we often rely on Yelp or Trip Advisor for whatever area we are in when we get hungry. The pocket Rick Steves guides are also good for this as he gives several suggestions for each area of the city. To be completely honest though, the food in Italy is so good, that you can't go wrong even in a "bad" restaurant. You will still enjoy fresh pasta no matter where you land!
I hope this helps at least a little. This was one of our favorite ABDs (well, each one we've done has been a favorite tbh). It is so well planned out and paced and the access you get is over the top amazing. You will have a wonderful time no matter what you do!
