Yosemite National Park is about a three hour drive east of San Francisco. And probably much more worth seeing than L.A.
If you don't want to drive all the way to Yosemite, SF has some good nature scenes of its own. You can drive across the Golden Gate Bridge and head about 30 minutes north to Muir Woods. There are plenty of redwood and sequoia trees up in that area.

Monterey is a beautiful city a couple hours south of San Francisco. The aquarium is top notch, but just taking the time to walk down Cannery Row is pretty cool.

Sticking with broad sightseeing, Lake Tahoe is about four hours northeast of San Francisco and it's another beautiful place to see.

Twin Peaks in San Francisco is one of the tallest points in the city. You can drive up there and park and it offers a beautiful panorama of the city (both during the day and at night). Be careful and pick a good time with good weather to go up, though. San Francisco is notorious for its fog, and it can be kind of scary driving up the mountain when you can't see more than a foot in front of your car.
Twin Peak

I lived in northern California a couple years ago, so I'll try to think of some other stuff you'd be interested in.