Having driven the coast many times, I can tell you that it starts to get really pretty mainly after Morro Bay/San Simeon and north from there on. Problem is that most of that area lack airports should you want to stop. Big Sur area has no real good coastal airport. However, if you venture up the coast north of San Francisco, along Hwy 1, the scenery is stunning and in my opinion even prettier than Big Sur. It's also full of airstrips. Don't miss Shelter Cove and Half Moon Bay is a good way to get into SF with a small plane.
I'd start in LA and do the whole coast up to the Oregon border. The huge 2000 year old Sequoias up in Humboldt State Park/Avenue of the Giants will just silence you. It's impossible to speak in their company - they're just majestic.