Keep in mind that, if you are camping, you must camp in an official campground in the most-visited National Parks such as Yellowstone, Yosemite, etc. (Death Valley is an exception and you can camp there if you are at least 2 miles from the nearest paved road or day-use area. There are some other restrictions listed on the Death Valley NPS website.) State parks have the same "campground" only restrictions for the most part.
However, "dispersed camping" (meaning you can camp just about anywhere) is permitted in most national forests and on Bureau of Land Management (BLM) land. The problem is knowing where the national forests and BLM lands are located. Some are obvious such as most of the Sierra Nevada mountains are in national forests (there are also Wilderness Areas but those don't have any roads into them anyway). National forests are shown on highway maps but BLM lands tend not to be shown.
If you prefer to boondock when possible, there are a series of guide books on where you can camp called the Frugal Guides:
The couple who wrote these guide books have guides for California, Utah, Texas, Arizona, and New Mexico and the guides can be purchased from their website as .pdf "books". We have the ones for California and Arizona and they have a lot of information in them.