Usually it is impossibly to find a free parking space in Napels. Even if you DO find something, that looks like a parking space, think twice! I have paid two penalties (but my car was registered on my friend from Napels, I hope they are more easy with the tourist cars with signs of other country). Try to use public transport, your feet or be there in August (thats when there are the best chance of finding free parking space since city is abandoned - but I havent promissed anything.)
Look at the picture: there is only ONE PART of the car on the right corner (irregularly parked, though). Amazing! The street is empty for a while.
I really recommend renting a scooter, if you want to get somewhere fast. Dont forget to wear a helmet, since you will be taking risk of crashing with a car! But a scooter is the fastest thing on the south of the Italy. Try not to ran out of gas in the middle of nowhere (beware of the possibility of broken empty gas indicator). Parking a scooter is very easy. You have special parking places (usually full, but you can squeeze in your vespa with a few gallant moves)and you can also improvise elsewhere... However, I have gained a very ugly scar on my knee (well, there goes my modeling career) - the last day, when I fall of the vespa at moderate speed.

