My wife and I have camped around the west (mostly arizona). I've never had a problem in National Forest or BLM lands. Find a quiet place and enjoy.
In this part of the world you need to be careful on the Indian Reservations. They have their own rules and "due process" does not apply. Check with the locals before you pitch your tent without a permit.
Have a great trip.
This is my only chance to assemble a disreputable past