California has some rigorous laws against vagrancy and homelessness and depending upon local ordinances or just plain bad luck you could be in for a nightmare. If you have to do it, try to be outside the city limits.
Based upon what you wrote, you will most likely have a license plate that identifies a rent-a-car. That will flag up as unusual for anybody who takes notice, like the police. It means it will be more difficult to 'blend in'. That might be enough for an alert cop to justify checking you out on 'probable cause'.
Someone could report, for example, that you appear to be an unresponsive person inside a vehicle, and that will bring the police to check you out.
Or alternatively, a local whacko might decide you'd be better off without that shiny new car, your cash and valuables; and in the best outcome the police will show up and start asking questions. In the worst outcome, you're dead so it's a moot point.
If you get caught, you'll have to demonstrate that you're not 'homeless' and not under the influence of drugs or alcohol, and most awkwardly, that you're not soliciting for prostitution. If they are not satisfied, it's off to the nick with you. If they see you have an Italian passport, DHS will get involved.
And heaven help you if there was a violent crime in the area and they are sweeping the area.
READ THE LAWS: http://codes.lp.findlaw.com/cacode/PEN/3/1/15/2/s647
You also need to read the fine print on your rent-a-car agreement. If they disallow sleeping overnight, the contract may become invalid, and then the attached insurance and what-not might be invalidated, and that means you are in a big time problem if you get caught.
Other than that, fine!