Will you have a car, or will you be using public transportation? If you have a car, you can get to some awesome places within 20 minutes of the city as well. Also, for how long are you staying? In addition to the wonderful ideas suggested above, I would add some local flavor to your stay:
1. The Farmer’s Market at the Ferry Building. Awesome views, great food, window shopping awesome local vegetables, people watching.
2. Stairway walks. I hate to put this out in public, since these secret stairways are a treasure, but since we fluther together, I feel obliged to share.
3. Mural walks in the Mission district. Not only will you see some beautiful local murals, but the Mission district is definitely an area to explore and experience on foot.
4. No visit to San Francisco is complete without a visit to Chinatown. Eat at a restaurant without an english menu… Do some tea-tasting at a teashop.
5. If this is your thing, you can visit the Haight-Ashbury neighborhood. It has become somewhat commercialized and gentrified, but still, it is a window back to the 60s counter-culture movement. Also, conveniently located next to Golden Gate Park and the Japanese Tea Garden (word of warning, the tea here is very expensive, and frankly, weak and watered down).
6. Hiking the Land’s End Trail in the Outer Richmond. The has the best views of the bay, and is a beautiful walk to boot (more info here). At the end of Land’s End is the Sea Cliff neighborhood. If you like to walk around imagining what it would be like to live in a $10 million dollar home with views of the bay, this is the spot.
You will notice that most of these things are not tourist spots per se. You might want to mix and match seeing the so-called main attractions like the Golden Gate Bridge and Alcatraz with more local events. I would add that the advantage of the walks is that they come at just the right price… free! Have fun!