Is this a OW or RT between L.A. and Vancouver? You could take about a week+ driving up and another week+ driving down. I'd recommend heading slightly inland to the west side of the Sierra Nevadas and drive up CA route 49 ('49er gold rush trail) which takes you past/through/by Yosemite and many old gold rush towns as well as some wine country (see it while it's still somewhat quaint and relatively unspoilt/undeveloped). This will take about 2-3 days (preferably 3). From there, switch to CA 89 that'll take you through Mt. Lassen and from there to Weed and up to Crater lake. I'd budget at least 2 days for this At this point, you can stop or drive up I-5 to Vancouver (1 day at most unless you want to stop).

On the way back, you can drive down the coast (around Olympic peninsula would be nice but not sure how much you see) and basically follow the coast all the way down on US 101. 1 week would be nice. You can go inland north of S.F. to visit Napa/Sonoma.

Of course there are many other things to see but this will give you a good taste of the west coast.