Really???? I would seriously look into that offer as I have never seen anything close to that price so I'd want to make sure it's "real" before I did any planning based on it. Other costs to consider besides whatever the "price" is include local fees and taxes, second driver fees, and other things paid locally. And of course you need to consider parking, tolls, gas. Insurance. Different pick up and drop off location fees.
But assuming you really do find an amazing deal you'd need to consider where you want to go. You don't want a car in any city - first off you can't drive into the center as most towns (even small ones) have 'limited traffic zones' and if you drive in them without a permit you incur large fines (usually sent to you via the car rental agency months later). But besides the basic problem of driving in unfamiliar cities, parking can be very costly and inconvenient.
However, a car really is nice to have if trying to visit small hill towns in Tuscany/Umbria or exploring mountain areas like the Dolomites or Val d'Aosta. Since you are flying into Naples are you planning to visit the Amalfi Coast - I would NOT want a car there in mid summer. But if you want to venture over to Puglia then a car is an asset and driving around there is pretty easy.