Do the tour of Alcatraz in SF. You often need to buy tickets a few days ahead, so be sure to pick them up in time. It's a typical tourist thing, but worth it.

Head out to Napa (a couple hours north of SF) and tour the wineries. There are more wineries than you can possibly visit spread out over some very beautiful countryside in that area. Some of the wineries sell some specific wines only at their tasting centers. I have a soft spot for the winter harvest Chardonnay by Kendall-Jackson (it's a sweet desert wine without being cloying).

A couple of restaurants that I can highly recommend:

Baker St. Bistro (French/SF)
Zeyno's Grill(Mediterranean/Birlingame - down the peninsula from SF)
Trattoria Volare/SF-North Beach - Excellent Sicilian style food Their main web page seems to be down. Here is reviews and address
Also
WWW Stella's is just down the street. Do NOT buy anything other than a cannoli here. It's just a block or two away from Volare's though. Down a restaurant row.
Gullivers/English style prime rib - Good food,but the decor is the biggest draw. Everything is done up based upon Gulliver's travel. They have a guy playing the piano most of the week (check dates with them) and they all dress up in english style dress

I know more, but that should be you started and I have to run.

I agree, very beautiful there.

OK, wanted to add a few more.

First, all the standard tourist stuff in SF is worthwhile (I'm assuming you know what that is, if not, I can drop them in here). If you do Pier 39, there is one thing a lot of people miss...Namely an old WW II sub is permanently docked down there ( a pier or two over), buy a ticket and do a walk through on it. It will not take that much time and I thought it was pretty enjoyable.

I would also mention the Winchester house. It's reasonably well known around here, but it doesn't get the kind of fame Lombard st or the Golden Gate bridge get. Basically when winchester (of gun manufacturer fame) died, his window went crazy. She thought the ghosts of all the people killed by winchester rifles were out for revenge. So, she built a house designed to trick them into walking into walls, etc. It's basically a crazy house built by a rich crazy person. It's technically in San Jose, but that is only an hour from SF.

winchestermysteryhouse

I wanted to also point out the San Diego zoo. Out of my area a bit, but it's absolutely impressive. If you start as soon as it opens and spend all day there, you will leave feeling like you saw a lot and still missed a lot. Not a bad way to spend a day.

I have to ask...

I'll dispute that. There's a Thai and Japanese place in the Santa Cruz area that I've never seen beat.

If you can drive a ways, the Grand Canyon isn't too far off. Not a lot to see in California aside from the redwoods, plenty to do, but really not much to see.

As for San Diego, I'd go for the Wild Animal Park over the San Diego Zoo... unless you really prefer the Zoo experience.

California is probably the greatest state for sight-seeing, over all in these United States.

And I agree with Brillig that the Wild Animal Park is better than any zoo.

Other west coast cities have their dining jewels, but no other place on the west coast has the depth or breadth of SF dining.

On the upside, coming over from the Netherlands (the OP) should give you a nice boost in real spending with the current exchange rate. None of the places I listed are super expensive. A full dining experience (Appetizers, meal, bottle of wine for two, dessert and an after dinner drink) should stay under $50 a head at the most expensive of them.