Since May 1 is Labour Day in Europe. What will transportation, museums, etc be like in Rome and Venice that day.
Transportation will operate on a Sunday/holiday schedule. There will be still be plenty of trains and buses running. The Vatican Museum will be closed but other than that, business as usual as far as the sights go.
I was in Rome on Labor Day a few years ago. The buses stopped running in the latter part of the afternoon, and it was very difficult to find a taxi. I don't know if that's changed. I suggest doing things in walking distance from your hotel on that day.