Rome - We much prefer hotels in Rome (we've stayed at several, though none of them at the price point that you have) in the area of the Pantheon and Piazza Navona. It's more centrally located for daytime tourist activities, and it's wonderful to walk between the two, as well as the Trevi Fountain, at night. There are also several great gelaterias in the Pantheon area! I think the Capo d'Africa is less convenient for that kind of thing. We took our 10yo daughter to Rome (and Florence and Venice) last fall, and she loved the location of our hotel.
Florence - I'm not familiar with the area of the Principe, but it's definitely not real close to most tourist sites. I'd choose something closer to the area of Piazza della Republicca (and, again, to several magnificent gelaterias). Our daughter loved spending time on the Piazza in the evening, listening to (American) street musicians.
Venice - Your location here looks good, very central, maybe a little busy, but ideal for easily getting to many of the most popular tourist sights.