Roadhound has ventured a route, and I think it is generally excellent. I also prefer the east side of the Sierra Nevada (US395) over a trip into the LA Basin and up the California Coast, but I had the impression you were sort of committed to Sunset Strip and Big Sur.
Let me present an argument for missing Big Sur. It is a beautiful area, but in my mind no more so than the northern California and Oregon coasts. And it is crowded as the dickens in the summer, meaning traffic (often slow). I think you can get all of the costal beauty and interesting coastal towns you can imagine on your route without Big Sur.
Of course if you must see Sunset Strip, then the California coast is a nice, though busy drive. But if it were me, I would take US395 (given your plans to see the northern California and Oregon coasts). If you have ever seen any old American Westerns you will recognize the often used movie site at the Alabama Hills near Lone Pine, and I promise you don’t have Mt Whitney in England! Then the drive over the Tioga Pass into Yosemite is like Snowdonia ten times over. And Mono Lake is a unique site.
I have the impression you may be young (I know you are younger than me!!!

), and I want to make another argument for doing US395. It is the “we took the road less traveled” and had a unique adventure. We discovered the “real” America. You can visit every site everyone else visits, or you can have bragging rights to places and experiences few overseas travelers even know about. You sort of have to decide which way to lean.
If you take US395 I can give you some little known specific locations you will want to visit. For example, one of the most poignant is the Manzanar internment camp where we imprisoned Japanese American citizens during WWII. There are spectacular volcanic formations in the area, and at Tom’s Place a genuine old, unchanged small western resort.
I want to make one more observation, and I don’t know how to do it without sounding negative

. Going from Las Vegas to Hollywood, you will enter the LA Basin traffic and mayhem at Cajon Pass about 20 miles out of San Bernardino, and you will be in the bowels of the freeway traffic pattern for 80 miles to get to Hollywood., Then you will be in urban sprawl and congestion all the way to Ventura and beyond as you escape. You really have to have a good reason to suffer that mess voluntarily.
Having “downed” the Sunset Strip and Big Sur route, let me now suppose you have good and compelling reasons for going that way. As you travel north plan to spend a little time exploring Santa Barbara. It is a big city, and pretty pricey, but it has used some of its wealth to preserve its Spanish – Early California heritage. The mission, the old downtown, and the beach front with its piers and restaurants are worth at least a few hours of your time. It is sort of Spanish cosmopolitan, or Early California chic

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It would be a shame to take this route without visiting at least two missions. The one at Santa Barbara is fully “restored” which makes it like it never never ever was. But it is beautiful and interesting.
Given that you would leave the El Camino Real at San Luis Obispo to go toward Big Sur, I think I would suggest as a second mission La Purisima (Mission La Purisima Concepcion de Maria Santisima ) near Lompoc. It is less restored and retains some of the feel of the original….I like it for that reason.
On the off chance that you end up staying in Lompoc for the night, take a trip to Jalama. It is hard to find on a map, but there is a county park there and I think the little restaurant and store are still in business. It is a surfer’s site, and windsurfer paradise. Down the beach is the Point Conception Lighthouse. Watch for the tide if you hike there.
On the way to Jalama you will be traveling the California outback as it was in 1840. It has been perhaps ten years since I was there, but since it is a huge old land grant, it probably is unchanged. It will probably be the only place on your trip where you can get a feeling for the unspoiled Early California life style. When I was last there ten years ago, there were still vaqueros riding the range…..but I imagine that day may be gone.
As you go north from San Luis Obispo on California 1 you may want to visit the Hearst Castle, a monument to his wealth. It is truly a beautiful, magnificent site, well worth a visit, but you have to book a tour well in advance (remember those crowds I mentioned?)
I have not been to Big Sur in 25 years (I get to spend time on the Oregon Coast often) so I will end this here and see what you think.
Oh, BTW, I live in Olympia, Washington, and know the northwest very well...so when we get there in our discussion, I'll give you the inside story

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Keep the Show on the Road!
Dave