i wouldn't want to tour inside the cities.
research italian trains, especially the local commuter runs.
have a base in the big city. early morning before the rush, take a train to an outlying area and spend the day in the countryside, ending up early evening either in the same town/village, or another town/village on the commuter train line. after the go home rush, take the train with your bike back to the big city.
i'd do two large cities as the endpoints, with a smaller town or village in between. in that case all three of you can spend a few days in a small town in the countryside, and at least one day rent bikes for the other two.