From LA there are two great ways to go North. Coast or Mountains. Unfortunately the state is sooo tall that only one is really possible. So you'll have to choose, unless you'll be coming back toward SoCal in the fall, then take the other route.
If you want to try a little of both, the best scenery would be to head up US-395 to the East of the Sierra's (Gorgeous!) then at Yosemite or Lake Tahoe turn left and head toward the coast at or near San Francisco. While the Central Coast is beautiful, the North Coast is awe-inspiring. In July, it will be hot getting to the Sierras, while the coast will be chilly,
One thing is almost no California State Parks have hook-ups, so be prepared to dry camp. On the other hand almost all Oregon State parks have at least electric and water. Of course, no national parks have hook-ups.
Here are some places to see if you do go up US-395, Convict Lake, Mt. Whitney, Manzanar Internment Camp, Ancient Bristle Cone Forest, Mammoth Hot Springs, Devil's Postpile NM, June Lake, Mono Lake. If you choose to go by way of Lake Tahoe, at least make a day trip up into the Yosemite High Country from US-395 in your Tow Vehicle up CA-120 through Tioga Pass. Bodie SP(ghost town), either take US-50 West from South Lake Tahoe or drive around the lake and take I-80 toward SF. US-50 is good if you want to see where gold was found near Placerville (lots of Apple Orchards at Apple Hill just east of Placerville, we go every year.)
Check out Old Town Sacramento (CA Railroad Museum, if interested), Napa and Sonoma Valleys, San Francisco, take US-101 North, Humboldt Redwood SP (drive along Avenue of the Giants), Redwood NP. In Oregon, near Port Orford check out Prehistoric Gardens, a tourist trap for sure, but you would swear you are in a scene from Jurassic Park. Our favorite State Parks have been, Sunset Bay SP, Beverly Beach, Fort Stephen's. Also check out either the Hatfield Marine Science Center or Oregon Coast Aquarium, both in Newport. The Tillamook Cheese Factory (to die for grilled cheese and tomato soup.) See as many lighthouses as possible. Eat lots of fresh seafood. The Astoria Column, Lewis and Clark National Historical Park.
If you do go inland at some point Mt. Lassen back in Northern California is beautiful, certainly go see Crater Lake, and once to Portland make the 1.5 hour trip to see Mt. St. Helens at the Johnston Ridge Observatory. Also, the Columbia River Gorge. I'm sure I missed a thousand other things, but that should get you started!
Enjoy the trip!
Tom