Yes, campgrounds and also backwoods camping. Many of these are government run (state and national parks) and many others are privately run. If you want to live in the backwoods, most parks have rules you need to follow, such as moving your tent every so often, disposing properly of waste, restrictions on lighting fires, and obtaining hunting/fishing licenses (meaning: do not carry fishing rod without a license).

Also, on every highway there are rest-stops and trucker rest areas. Some of these have pay-per-use showers and most have a parking lot you can park overnight in and free toilets.

The national/state parks are beautiful and are very welcoming to visitors.