I'd want to hire it as far from busy big cities as possible. The idea of damaging one, even if insured, would be so upsetting.
So to maximise this, you'd want to do it during term time (kids in school, less people on holiday), when there's good weather.
You'll want to pick up the car outside of rush hour, so around 10am, and still have a couple of hours to get out of town before the lunch time rush starts.
The best mountains are in the north, bordering with Switzerland. The lakes are there too, for some different scenery.
This from an Italian luxury car hire website:
Every region in this beautiful, boot-shaped country is different form[sic]
the other. To hire a Ferrari in Italy will enable you to reach
everyone[sic] of those regions in elegance and style. If you are in North
Italy, looking for a car rental in Milan, rent one of our Ferrari cars
and drive along snow-caped[sic] mountains, beautiful lakes (Garda, Como and
Maggiore) and fascinating amusement parks. Don't forget to drive your
Ferrari to Bergamo, Verona and Venice! In the center of Italy you can
hire a Ferrari in Florence and tour Tuscany, including Bologna and
Pisa. This route will be dotted with green forests, round hills and
small towns that time hasn't touched. You can rent a car in the South
of Italy, and drive through delightful beaches, deep blue sea scenes
and enchanting islands.
Incidentally that site does quotes, but I couldn't bring myself to look, so I'll leave that bit up to you ;)