When? You do know that Hwy 1 is closed at Gorda so you can't drive all the way through. If you want to see Bixby Bridge you should go to Monterey and then drive down to the bridge, or further to McWay Falls (really, not to be missed), and then head back to Monterey. Take Hwy 68 to Hwy 101 and head south to Solvang.
If this trip is in October or later than the road will likely be open.
July or August
Have you already explored Big Sur? If not, Solvang is an inconvenient place to spend the night, as getting there would either require a very long day's drive (if you were to go via Big Sur) or short-changing Big Sur (which would basically take you away from the coast).
I would instead stay in the area between San Luis Obispo and Pismo Beach. Start by leaving San Jose early, drive to Monterey, then down Hwy. 1 to explore the coast. See the highlights (Point Lobos, Pfeiffer State Beach, Bixby Bridge, McWay Falls, lunch at Nepenthe). Then return the same way (Hwy. 1, north this time) to Monterey, then connect to inland Hwy. 101 south to your overnight stop. This is the detour to get around the road closure at southern Big Sur.
Exploring Big Sur can take all day, which is why the drive from Monterey to Solvang would just be too much on top of a day of sightseeing.
Again why are you trying to combine the big Sur and the LA trip ? Do you live in San Jose. Do this as a separate day trip please
Given the road one closure this will be too rushed
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You were referencing a news report from February 2017. 16 months ago!
For those of us who live on this planet and pay attention to more recent news: simply refer to what Susan said in #7. Ignore #9 and some way-outdated news article. If someone has his way, he may be telling you that somebody just flew a plane onto World Trade Center, or the Japanese just bombed Pearl Harbor.