If your camper is not too wide, in Florence, I would suggest parking along the Lungarno del Tempio which becomes Lungarno Colombo. There is street parking that should provide lots of space... more parking as you keep going away from the center and it becomes Lungarno Aldo Moro. Map these so you see where they are ahead of time. If your camper is wide, then I would suggest Lungarno Aldo Moro from the start, on the side that heads toward the center as the parking there is diagonal and you can take up more space. You'll also see large buses park along this area and take up lots of spaces.
In Lucca, stay away from the center and go around the walls - the larger streets that lead away from the walls should offer space for parking.
Just remember, just don't park too far out and block traffic. As you'll see others do here in Italy, better to climb a bit onto the sidewalk and not have the camper out into the street ;-)