Uber

Ever thought of looking at Uber's website?
https://www.uber.com/cities/

Note that the Uber ap (and agreement) means they can monitor your location ALL THE TIME not just when you are using their cars.

Uber is present with the Uber Black service only in Rome and Milan.
Uber Black is a professional limo service aboard luxury vehicles driven by licensed professional limo drivers.
The more familiar Uber Pop (where the average Joe drives his own car for Uber) was declared illegal in Italy in 2015, as only licensed professionals can provide that service (you can thank the Italian taxi lobby for that).
Since the service is a professional luxury limo service, their prices aren't cheaper than taxis, but at least you travel in style since they use nice luxury cars.
Of the cities you mentioned, only in Milan it would be an option for you.