Skip Fisherman’s Wharf and Pier 39. LAME, overly touristed, and consists mainly of shops with overpriced junk geared at tourists. I grew up in SF and we used to go down there in high school to laugh at the tourists eating it all up and losing money by the handful. If you must go there, the only things worth doing/seeing are the SF Maritime National Historical Park (you can check out some old-timey boats) and pick yourself up half a freshly-steamed cracked crab.
Lombard St. (the crookedest street) is kind of lame, too. It’s like one block of a really zig-zagged road. I don’t get the appeal, myself, but it is kinda fun to drive down. However, the last time I took a friend on a tourist tour of the city, I was ready to run down the mobs of oblivious people wandering all over the place, holding up traffic. Perhaps you have more patience than I.
Alcatraz is cool, definitely check that out, but be sure to buy your tickets online in advance (from the National Park Service, so you don’t get ripped off) because they do sell out. Fort Point is also cool if you like history, and it’s directly under the Golden Gate Bridge, which is sort of nifty.
Honestly, there is so much to do and see there, it’s hard for me to pick just a handful. Golden Gate Park is beautiful and there are loads of things inside the park to see and do. There’s a bison enclosure, Stowe Lake (you can rent boats), a Japanese tea garden, the newly-renovated Academy of Sciences, botanical gardens, the De Young Museum (art), and on Sundays much of the park is closed to auto traffic. You can rent bikes and skates at places just outside the park (like at the end of Haight St.). Haight St. isn’t quite as fun as it once was, there is a smaller variety of shops and restaurants and I feel like the street has gotten even more dirty/sketchy than it used to be.
The Presidio is now a historical park and you can walk around and look at the military buildings and such. The Marina (esp. Chestnut St. and Union St.) is an affluent area with loads and loads of shops and restaurants. Pacific Heights is fun to drive through to gawk at all the mansions – this is where the city’s rich and famous live.
North Beach has some of the best Italian food you’ll eat in the U.S., Japantown of course has really super food and some interesting shops full of Japanese goods (Mifune is where the locals go for amazing and affordable Japanese food), Chinatown is very interesting and you will find the best Chinese food there (try the dim sum).
Anyway, I realize this is a lot of info, but I wanted to toss out a bunch of things you could pick and choose from, depending on your interests. Most of all, have a great time! SF is an amazing, beautiful city full of interesting characters. :)