I don't know Florence very well and can't comment. However, I do know Rome and Venice quite well and would say that location is very important. In Rome, decide on what you want to see - personally, I think the Russie Hotel is in a bad location because I have no interest in shopping or the Renaissance/Roman Catholic side of the city. I like the older city, the ancient Roman city, the pagan city, as well as Trastevere.

In Venice I would definitely avoid the traditional five star palaces - the Gritti, Danieli, Bauer etc. All are crawling with tour groups and while the map looks to be a fab location for all hotels you will quickly tire of the noise and the hordes of tourists, especially when a big cruise ship is in the lagoon. If money is no object the Aman Canal Grande might be the best option, though I don't fancy it myself, especially not after that Clooney circus. We last stayed at the Ca'Sagredo which we adored, as many people on this Forum seem to.