Lots of people do this, some every day, and they blog and vlog. Their hashtag is #vanlife. There is plenty of stories and advice.
Varies dramatically depending on where you are. California is very large (bigger than Italy, Switzerland and Austria combined), and so it has two very distinct personalities: rural and urban California.
Rural
Rural means lots of long-haul driving, and drowsy driving. As such, they provide places for people to sleep "on the road".
In rural travel, your trifecta are rest stops, truck stops (aka travel centers) and RV campgrounds. RV campgrounds must be paid for. Other than that, you are looking for places lots of trucks congregate, because they are doing the same thing.
Some rest stops are informal, essentially chain-up areas which the trucks have colonized - in that case, park to be seen as they are not expecting a 4-wheeler in their midst. The best are truck stops which have been gussied up with a pretty front area for automobiles.
Lots of people have good luck with small-town Wal-Marts, I've never had a need due to other options existing.
Keep in mind, these things will not exist in the city. There are no Love's truck stops, but there are plenty of Starbucks.
In the city - oh boy.
Because of the sheer density of urban California, and its symbolism to starry-eyed dreamers, things are much harder than even normal US cities. So many are homeless-with-car, and they need a place to park and sleep, and nobody wants them. Where they congregate, trouble follows, along with police.
So if you are trying to car-camp in the city, you are fighting this enormous prejudice, and you are better off getting a paid campsite or better, a hotel room if able. Not least, for the value of your time - given the cost of getting to the US, your limited time is fairly expensive! That said, it can be done.
A weird cultural thing in the US is Walmart. Walmarts which are open 24x7 tend to be tolerant of #Vanlife campers passing through. However they don't always have a choice - sometimes their mall regulations, or their city regulations, will not allow it. You park more toward the outside of the lot, so other customers aren't walking by your car. If you see a community of campers you are probably OK.
There are also areas in each city where this is grudgingly tolerated moreso than others. In San Francisco, that's the park side of Golden Gate Park, particularly on Lincoln rather than Fulton. But remember what I said about time?
These possible campsites are far from downtown. Between commuting, parking, and dealing with grooming and bodily needs, it'll cost you 2-4 hours to camp out in Golden Gate Park instead of an SF downtown hotel or near-downtown AirBnB. Every nearby business violently hates #VanLife people, so "borrowing a local business's bathroom" is not gonna happen. And if a City cutie falls in love with your accent, you are not going to have an enchanted evening.**
Don't forget AirBnB. California is its birthplace and has a high density of participating homes.
Edit: we just had a change in the law. Yesterday, the Ninth Circuit Court ruled that it's unconstitutional to roust and arrest people sleeping on the street. This will likely reduce police hassles of people sleeping in their car.
The Ninth has a bit of a reputation for being an activist court (and a bit left, just like the coast it serves), so it's yet possible this will be reversed by the more conservative Supreme Court.
**irony is, cutie was kinda hoping you had a place, because due to the same market pressures, they live with parents, in a crammed roommate share, or an hour away.