First trip to the US

First, before flying to San Francisco get online and reserve tour tickets for Alcatraz (Alcatraz Tickets & Tours - Visit San Francisco's Famous Prison)
If you're set on driving down Hwy 1 along the coast then I'd definitely recommend the following:
* Hearst Castle in San Simeon (Home - Hearst Castle)
* Monterey Bay Aquarium (Monterey Bay Aquarium – Official Site)
* Big Sur (Big Sur California, Lodging, Camping Tourism Information

But if you want to see some truly remarkable nature and scenery, I'd drive south another way and visit both Yosemite National Park and Sequoia National Park. You won't be disappointed.
* Yosemite (Yosemite National Park (U.S. National Park Service))
* Sequoia (Sequoia & Kings Canyon National Parks (U.S. National Park Service))

What dates are you going to be in the Los Angeles/Orange County area?