Well then I'd probably hit the beach chalet for brunch, drive through golden gate park, maybe stop to see the casting pools or bison, head to the gg bridge overlook and look around, drive from there to Alamo square to see the painted ladies (just drive by, don't stop), drive down Lombard on your way to a garage in north beach.
From there you can explore on foot north beach (obv), Chinatown, and fisherman's wharf. North beach has things like beat museum & city lights bookstore, dive bars full of European tourists, Italian restaurants, etc. You can also grab a sandwich at naked lunch or molinari's and take it to the top of one of the hills with great views and pretend you're Kerouac.
Chinatown is obviously Chinatown.
The wharf has wackys favorite animals and clam chowder and great views but is super touristy. This:
http://www.museemechanique.org is kind of a quick free weird thing to do if you have time. You could also throw in a cable car ride to Chinatown which is easily my favorite tourist thing to do.
After that I'd probably go to brainwash cafe in soma for some open mic comedy:
http://www.brainwash.com/index.htmlThat's a lot for one day but you pretty much hit most of the good stuff unique to sf.
Other things to hit:
The Mission/Valencia street/Dolores Park
Restaurants (I really only eat nice meals in Oakland so I'm not much help here)
And I guess that's it. Come to think of it, there's not all that much to do here. I don't get why so many euros visit