If you're going to have a car and don't mind a fair bit of driving in one day (probably 6 hours round trip), the Monterey to Big Sur area is one of the most beautiful places in the world. While a little long, about 2-3 of those hours will have some of the most amazing scenery you'll ever see, so it makes up for having to sit in a car most of the day. If I had a week in San Francisco and access to a car, that would be right at the top of my list.
Also if you have a car, the area on the north side of the Golden Gate Bridge is pretty nice. You can check out old growth redwoods in Muir Woods and head up to Stinson Beach which is a pretty cool beach town about 45 minuted north of the city.
Other than that, there's lots to do in the city itself and I think everyone else has given you a pretty good handle on things. There are lots of fantastic places to eat in the city with pretty much the best of any kind of food you can imagine. Chinese, Italian, Japanese, Mexican, burger joints, there's great food of every kind.
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