Golden Gate and Alcatraz are must-sees.
*Many people rent a bike to cross the bridge, riding through the park and past the old Army flying field, and then return from Sausalito by ferry. My fiancee and I did that a few years back, and it was a hard ride at times but well worth it.
I don't know how busy it is now, but when we did it there were so many people walking across the bridge that we ended up walking our bikes on the bridge itself.
Tons of places rent bikes for this excursion and include a return ferry ticket in the price.
*If you want to see Alcatraz and not just sail past it, make sure you take
Alcatraz Cruises by Hornblower, the only excursion line with the National Park Service concession to land on the island. Other excursion lines advertise Alcatraz but only sail past the island.
I'd add:
*eating at least one meal at the Ferry Terminal at the head (or foot, if you're so inclined) of Market Street, where there's some very nice restaurants.
*Chinatown, including at least one meal if you like Chinese food.
*City Hall, which is very impressive. Weddings are performed weekday mornings (San Francisco is a county and a city), and couples get married or at least stand for photographs on the grand staircase.
*Cable Car Museum, which is also the actual engine house for the cable motors.
*The cable cars themselves, of course. They're not just a tourist attraction but handy to get around parts of town
(map) but the fare is $8! The work-around for this is to buy a Muni daypass, three-day pass, or if you're there long enough seven-day pass. Good for the light rail and buses as well as cable cars, but a lifesaver if you end up using the cable cars to actually get around.
*Lombard Street.
*Fisherman's Wharf. Yes, it's cheesy and touristy, but the sea lions at Pier 39, the chocolate at Ghirardelli's, the sourdough bread at Boudin's, and the seafood restaurants are real.
*Buena Vista restaurant, near Fisherman's Wharf and at the end of the Hyde St. cable car, is authentic and rightly famous.