vicinities; Golden Gate Bridge and the park, the largest China Town in the North America, bigger than NYC one. You may go to north of the GG Bridge to Mill Valley by John Muir State Park. There are some art galleries and some beautiful seaside communities. Or you may take a zigzag ride through mountains to Half Moon Bay to taste some King crabs, or go to Fisherman's Wharf to have nice dinners and do some shoppings. You may take ferry to Alcatraz.... Also you may go to the Japanese Town for some sushi prepared by people from Shanghai!
I am planning to go there again in the next two weeks if I can get a last minute package. Normally I don't need a car in NYC (also because the rental fee per day for car is about $100!) when I am visiting. But in SF you definitely need a car (also in LA!!). It only cost about $25 per day to rent a car in SF.
Have fun!