Almost any municipality in the U.S. has something in their ordinances or housing codes to prevent living on the street or in other public places, whether in a RV, a car, pitching a tent, rolling out a sleeping bag, or just curling up in a shop doorway.
It is a matter of degree of enforcement. Big cities are actually where you can most often get away with this, because there are a lot of other street people out there, not enough enforcement officers to deal with all of them, considering greater crime problems keeping them busy. There are also legal aid groups working against enforcement of the laws directed toward this problem, as street people in some places are treated as a protected class.
In the suburbs, and medium size cities that don't have a street people problem, enforcement is usually on the basis of complaints, so what you can get away with depends on how conspicuous you are, how much you annoy people, and how nosy the neighbors. I would not try to camp on the street in any gated community or neighborhhod watch area.
Small towns can be even more of a problem, because everybody knows who belongs there, and activites of strangers are almost always treated as suspicious.
If you really need to park somewhere to sleep, safest choice might be to go to the police station and ask. You might be told nowhere, or you might be told where, an it is often the police station's parking lot, where they can look after your safety and keep an eye on your activites.
