Sucks bc the summer will be so hot and crowded at some places I would say ya need to see. But i would do a huge counter clockwise loop around the west from LA. Especially if your a nature geek.
From LA ya could cruise to Havasu, check out Joshua tree.
To the grand canyon, which is breath taking and a must see.
Up to Zion and southern Utah are amazing and other worldly.
East to CO to play in the mountains. Anywhere is good but if I had to choose the SW part of the state is prettiest.
North up to Wyoming to seenth tetons and yellowstones unique thermal features.
N to Montana and glacier if ya can.
West through idaho and the not very frequented Sawtooth mountains. Boise is a cool town too.
South through Washington and Oregon to play in the cascades.
Sequoia, kings canyon, yosemite and your way through California.
Stop in San fran for some dim sum and the muir woods.
Then back down the 101 to fly out!
Thats what i would do, could do it in 3 months and youd see a lot. But like i said, the NPs will be packed.
Have fun!