In Rome we stayed in Hotel Traiano
. It was very centrally situated, we walked to all the sights although the Vatican was a bit of a hike. The room was nothing special, but we did have our own bathroom, a portacot was provided for our 18mo and a single bed for our 3yo and breakfast was included. I'd stay there again. I wouldn't recommend walking there from the train station with all your luggage and two small children in pouring rain though.
Haven't been to Venice so can't comment there, and we rented a flat in London.
Enjoy your trip.