I will be flying to Los Angeles in mid-June for 10 days and want to see as much of the west coast as possible.
If you actually stayed on the west coast, 10 days would be a reasonable period of time. However, your plan calls for trips to Grand Canyon and Rocky Mtn NP and your roundtrip mileage will easily exceed 3000 miles. A lot of miles for a solo roadtripper who also expects to camp along the way. Do you really need to travel that much? Are you used to driving 10+ hours per day in the mountains?