Take the Eurovan. The safest free spots to park it for the night to sleep are large chain truckstops (such as Flying J) at Interstate exits away from large cities. It's best to get permission, and throw a little business their way (fill your gas tank, eat breakfast in their restaurant) - and you can buy a shower ticket for 10 bucks or less to get cleaned up. The next best option are paid campsites, either commercial or in state/national parks.

It's generally not legal to park overnight in an Interstate rest stop, and it's not particularly safe either.