Truly depends on what your into...hmm...
Tickets for Alcatraz Island go fast, or rather, early fast; if your thinking of it, you should buy tickets online ASAP, as tickets tend to fill up fast. It's a self guided tour with a headphone and a locked mp3 player that you pick up inside the island.
Western side of SF is typically foggy, eastern end is the sunny side. When trying to get views of the golden gate bridge, most of the time it is covered by the fog
There is a parking lot area just before the bridge toll (free but can get packed); walking the bridge doesn't take too long.
Fisherman's wharf is a tourist place/trap. Can rent bikes to bike towards the bridge, rent a mini-go-kart and follow the map for some stuff to see.
Golden Gate Park; You would want the Eastern end of it, you've got the museums there, the Botanical Garden, other stuff, Japanese tea garden (small but cheap place to go into).
Kite related events- BASKL is having their competition this Saturday at Ocean Beach (directly west/next to Golden gate park); SF Kites have their fun fly on Sunday at Marina Green, you can see the bridge from here too at the background if its not covered by fog.
I'll post more as I think of them