I want to plan an ultimate road trip to every state in the US. I am faced with researching each state for their laws regarding sleeping in owned vehicles. Is there an easier way to gain this information?
Rules regarding sleeping in a car in a city will be defined by that city. Rules regarding sleeping in a car outside the city will be defined by either the county or state or both.
As a general rule of thumb you will find very few cities that allow sleeping in a car on the streets. People get away with it by parking in less public spots, alleys, behind shops, etc. But the downside is that safety can be a concern in bigger cities in these out of view places.
Outside the cities many highway rest stops and pull offs allow you to sleep for a while, but patrolling officers may pay you a visit if they see you for long periods of time (8+ hours). You will often see truckers pull in for a few hours nap.
Most campgrounds have no rules against sleeping in your car, so small towns with public camp grounds will be an option. Commercial camps, government camps in forests, national or state parks, etc also are usually OK with you sleeping in your car (but cost money which seems like might be a factor for you).
Many cities and counties are passing laws designed to solve the homeless problem by motivating the homeless to leave the area. One of the methods has been to make it illegal to sleep in cars or other places.
It is my opinion (and usually the courts agree) that these laws violate the homeless person's constitutional rights. However, that doesn't stop the local "authorities" from making it necessary for you to go to court. And, in court, the fact that you are not homeless may make many of the rulings inapplicable.
Thus, Tom's advice to look for places away from cities is the easy way out. But if you are interested in reading about some of these laws and challenges, here are some links: