In general, National Forest lands allow what they call 'dispersed camping' anywhere except in the high-use areas and near existing campgrounds. Best to check with the rangers at a station for the specific forest for their rules, locations, and suggestions. Campfires away from campgrounds may not be allowed, due to our ongoing drought conditions.
BLM and state land is generally OK, but it is tough to know just what land qualifies as it is rarely if ever marked. Private land is almost always off limits and Indian reservations always forbid non-member camping.
In any case, be well off the main road. Out of sight is also out of mind.
Agree with Poohbear, use the existing campgrounds whenever possible. If you plan to hit many of the National Parks or Monuments the annual pass is a great option, even better if you are a senior (like me) and thus eligible for the discounts. Advance reservations for camping is highly recommended, particularly if you will be there during the high tourist seasons. Weekends are always crowded.
The Rockies in June can be cold and wet, or beautiful, hard to predict. Expect the NW to be wet and the SW dry. Carry extra fuel as distances can be deceiving and the fact a map shows a named dot does not mean a town,or gas station, is there.
That said, California is in the midst of a budget crisis and has raised their user fees. Camping can almost be as expensive as a motel, so check ahead. The PCH is a great ride, but slow, so take that into consideration as you plan.
Have a great trip, and keep us posted. Photos are always appreciated. Check in if you have questions.