I would think six weeks would be about right to get a flavor of CA.
No one mentioned anything north of the Napa/Sonoma Wine Country, but the area from Sonoma to the Oregon border is larger than the entire state of PA and it is full of great little towns and sights.
It would be very easy to spend a week each in cities like San Francisco, Los Angeles and San Diego and areas like Orange County where Disneyland is.
But then you have the national parks like Yosemite, Death Valley, Sequoia & Kings Canyon National Park plus others, the desert resort areas like Palm Springs, northern beach cities like Santa Cruz, Capitola and Monterey, the Central Coast beach towns and the beach towns of SoCal.
Then you have the mountain region with Big Bear and Lake Arrowhead in the south, Lake Tahoe and Mammoth Lakes in Central CA and Mt. Shasta in the north.
You can also visit the highest place in the continental U.S, Mt Whitney at 14,405' above sea level and the lowest, Death Valley at 282' below sea level, in one day. They are only 85 miles apart.
As to what can you do in 6 nights? You have good recs above, but you don't say WHEN you are coming and that is crucial for getting the best advice because mountain snows close certain passes that can effect the advice and if you say "July" and you want to visit Yosemite you might be too late already to get reservations anyplace, they are limited and fill up fast.
November_moon had good basic ideas, let me steal and expand their ideas.
1) SF to LA using Highway 1
2) SF, Monterey/Carmel, and Yosemite
3) SF, Napa/Sonoma
4) LA, Santa Barbara/Santa Ynez valley
5) San Diego, Temecula Valley, Palm Springs
6) LA, Orange County
In any one of these ideas you'll feel rushed in 6 nights because there is so much to see, but it is a start.