Rome, Venice, Florence.. where to park a Rental car outside the city?

I have to ask why they will have a car when all three of these cities are connected to a fabulous rail network. And as rental rates here are so high, paying to park it for days is a very costly venture. If they must drive, they should drop it off when they arrive in each city and rent again on departure. It just makes economic sense.

"won't need it in Venice, Rome or Florence, in my opinion"
In Venice, they can't use it, unless it's amphibious! There is a large (and expensive) car park at Piazzale Roma, on the edge of the city. Google "Piazzale Roma parking". This square is the only place on the Venice islands cars are allowed.

Railway stations (Train terminals) are usually central locations, and have limited if any long term parking. Airports are an option, but they are perhaps further out than you want.
"They could get cabs or busses from those places into the city, I would assume?" - or better still trains.

As Laurel says, why have a car in the first place? Where is your friend going that needs a car? If (s)he is just going to those three cities they can travel more comfortably, quicker and cheaper by train. Then just hire a car for those locations which need a car.

OMG - dump the rental car.

Since it appears that your friends are still on the planning stage, maybe they can arrange the rental accordingly.

Strictly for those 3 cities they wouldn't a car at all and they could very easily travel by rail between them and maybe not rent a car at all.

So we need to know more details on their trip so that we can better advise you/them. As a general rule, if one must absolutely have a car in those cities for otheri needs (I'm generally in that category), one should choose accommodations with parking outside the Limited Traffic Zone if not outside the city altogether. In the case of Venice, there are no hotels with parking (cars can't float either), so the only option is to park the car at one of the parking structures at Piazzale Roma/Tronchetto, unless you are willing to stay outside Venice, in a hotel with parking in Mestre or Padua and commute to Venice every day by rail (10 to 20 min respectively).

As mentioned above by Laurel, if one has to have a car, the most logical way is to rent on the way out of those cities and return it as soon as you arrive to the next town. As a result, starting the trip in Venice and ending it in Rome is a good practice. Florence and Tuscany would be in between. If one intends to visit Florence only, then I don't see why your friends would need a car at all, they could rely on trains exclusively. If they plan to stay in a countryside location outside Florence in Tuscany, then a car might make sense, in that case they would rent a car on the way out of Venice, drive to the Tuscan countryside location (visiting Florence as a day trip from that location), then proceed to Rome where they would return the car upon arrival (they don't need a car in Rome obviously).

As for Florence, there is no free parking within a fairly large radius from the center. The cheapest solution would probably one of the large parking silos; large and not too central ones like Parterre and Alberti have weekly tickets at 70 euros (to be bought in advance).

They need to plan their driving part of the trip separately to Rome/Florence/Venice. Why pay for a car to sit in an expensive car park?

Thank you everyone for your replies. We have been to Italy before and are familiar with these towns and know that you don't want a car while in them. Our friends are asking about parking because they want to drive. They know about the rail system, it's just their choice to drive. There is a flexibility with having a car that you don't get on the trains. We will cover all of their options, including costs. Thanks for the helpful parking tips.

Then the best option is to fly to Venice, stay there without a car. I hope your friends realize that cars can't go to Venice.
On the way out of Venice rent a car at Piazzale Roma.
Drive to Florence and find a hotel with parking (or parking arrangements with a local garage) outside the city walls (you can't drive inside the city walls, only residents with permit can).
Lastly drive through Tuscany all the way to Rome.
The car in Rome is a hassle to have too and large portions of the city center are forbidden to non residents as well). So return the car upon arrival in Rome and since your friends don't want to use public transport, they can use taxis. Fly home from Rome. Use a taxi from the city center to the airport (30 to 45 min depending on traffic)
I frankly don't see how a rental car can afford them flexibility when they are prohibited from using it in those cities.