In Rome we've stayed at Hotel Fontanella Borghese a number of times and have always been pleased. It's very nice and the location is great. You can walk to The Spanish Steps, Pantheon, Nuvona, even Vatican City. The staff is friendly and helpful. Ask for a room overlooking the courtyard as rooms overlooking the side street can get noisy. Check them out at their web site which is www.fontanellaborghese.com. If they can't accommodate you they have a sister hotel closer to the Pantheon called Hotel Due Torri.
In Florence we've stayed at Hotel California (yep, that's the name) and really liked it. Very nice and within walking distance of all the places you’ll want to go.
In Venice we really like Pensione Guerrato and have stayed there several times. The location is very close to a vaporetto stop, but far enough away from Rialto Bridge to not be in the mob scene. Iit does have some stairs to climb. If you book there let us know and we can give you directions that will eliminate a lot of walking with the luggage.
With all of the above we send an email directly with our request for a booking and get an answer in 24 hours or less.