WOW, SF is such a great city and there is so much to do.
Reefbaby hit on a lot of the things to do.
Last time we were there, before my sister moved. We took a great bay cruise. It wasn't very expensise and it sailed under the Golden Gate and around Alcatraz. It's a neat way to see the bay and a lot of sights at one time. You can purchase tickets at the Warf.
We also love to go to Ghirardelli Square and get sundae's in the summer and
hot chocolate in the winter. Its not too far from Fisherman's warf. It is the origianal factory and pretty neat. Its also cloease to where the main cable car station is.
I second the Farmers Martket on the Ferry Pier. It is a great place to pick up from artisian beads, cheese and wine and have a picnic (although it may be pretty cold up there this time of year)
You definately do not need a car, but if you do have time to head down to Monterey (abouts 1.5 hours drive south). It's is a beautiful drive down the 101/PCH and they have a great public Aquarium.
Have Fun!
John