We have taken an almost-9-year-old (our son) and a 10.5-year-old (our grandson) to Italy, and of all the places we went both enjoyed Venice the most. Both were in Venice for a week. There is nowhere on earth like it. Yes, parts of it are crowded, but much of it is surprisingly free of other tourists --- in December right before Christmas, we were all by ourselves visiting Torcello, the Bobolo staircase, a gondola/boat museum, and trying to find the narrowest alley. It really helps to get up early and go out before daytrippers and people eating hotel breakfasts do. We never ran out of things to see and do, despite skipping almost all of the "art stuff" and churches, and in fact did not do many of the things on our list such as going to the beach and on a lagoon boat tour. I made our grandson (and our 6-year-old granddaughter) booklets of photos of 50+ Venetian sights and experiences and they enjoyed discovering these things (e.g. the last two bridges without railings, an ambulance boat, various signs forbidding stuff, black spaghetti, etc.) and earning points. To reduce competition, the rule was that if either child saw a thing, they both got the points for it.
For trips with kids (and trips for just my husband and me), we have found that instead of alternating busy days and relaxing days, it works best for us to have full mornings, long lunches far from the tourist hot-spots, and free afternoons. Except for a few playgrounds and a ride on a small goofy rollercoaster, we didn't do any specifically "kid" activities, just regular Venetian things we knew the kids would enjoy, like bell towers and vaporetto rides. They loved spotting "naked people" in the mosaics inside San Marco basilica.
