Just returned from VFR trip. Wonderful all around. I'll try not to repeat what's in the other posts but highlight other things. Weather was cool, sometimes raining, but never sweltering hot, so I can't imagine midsummer standing in the waiting lines with no shelter. Just so you know. Please excuse my spelling of names of sites: I'm doing it from memory.
In Venice, the "Secret Itineraries tour" sponsored by the city were sold out BUT I found on Trip Advisor the same thing, but at about twice the cost (just for Doge "Secret Itineraties", not those including St. Mark's). We got a first-in-morning tour with a competent guide, had nearly no line, and saw all of the behind the scenes locations in Doge Palace, which were frankly more interesting because it had more to do with the political structure and management of the region, and then when you're done, you just go right into the Palace and spend as much time as you want. I considered this a worth while investment.
The boat tour on the lagoon to the island of Burrano -- nothing special here. The best part was the return to the public docks and seeing an Italian argument concerning one boat cutting the line in front of us, the five other boats in line, and the dock manager. The island is cute, but I wasn't convinced the time there could not have been better spent elsewhere. Though famous for lace, the real stuff is $$$$ so we didn't do much shopping. Seemed like it was an excursion site for Italians, who were also on vacation that week.
Florence: we did the Piti Palace and just a touch of the gardens. In retrospect, coming back and seeing the Bargello (which we missed) would have been a better choice. If you love (not just like) Renaissance art, then go. If not, go elsewhere.
Rome: St. Peter's church. The tour went at a time when we would not get in soon enough to be able to enjoy time in church before the Vatican museums. We were staying an extra day so we went early early and waited for only 30 minutes. Midday, the wait was 2 hours. Don't miss going down into crypt where all the dead popes are. The Vatican museums: packed with people but unbelievably packed with history and art, then ending in the Sistine Chapel. All of this is on the tour. Rick's audio walk in Trastevare was worth it. Got you away from Big City Rome.
Climbing things: I recommend not climbing St. Mark's dome in Venice, nor the Duomo in Florence, nor the Dome in St. Peter's. If you want good views, we were extremely happy with the Campanille tower in Venice (100% elevator and short line at sunset, perfect views), do the tower in the Palazzo Vecchio in Florence, and do either the Victor Emmanuel monument in Rome (good steps and elevator) or St. Angelo fortress (all on foot, but very gradual). The others have long lines, all steps, not for the claustrophobic.
Tourist-free viewing: Get up at sunrise. No one on the Rialto bridge. No one on the Ponte Vecchio or in the piazza. A handful of people at Trevi fountain. And you can see how dedicated the folks in Venice and Florence are about cleaning up after all the tourists.
Use your hotel clerk/concierge for restaurant leads for dinner for your nights not with the tour group. Their recommendations were always spot on.
Loved the tour, loved Italy. We'd go back. Enjoy your trip.