By all means, take the tour of Alcatraz. Amazing place.
I’d also second the Exploratorium. The cable car museum is worth a look, as is the Coit Tower. Even if you don’t get to the museum, you should try to ride a cable car.
South Beach is also a nice place to wander. Stop in at the City Lights bookstore.
Don’t bother with Chinatown – I’ve been to Chinatowns in San Francisco, New York, and Montreal, and they all look alike. Seen one, seen 'em all (though the French signs in Montreal made it slightly different).
As far as restaurants, you can’t throw a rock without hitting a great one. Pick a place; you can’t go wrong. I would say, however, my favorite meal during my visit there was Kiku’s of Tokyo (in the Hilton). Great Japanese food.