There are tons of things to do. I grew up here and still haven't done everything. Pier 39 and the wharf are tourist traps, so it's ripoff prices (but it has the only in-and-out in the city). It kinda sucks that you aren't 21 because it's been almost a decade since I was underage, and even then all I did was drink OE 40's at random spots like Tank Hill or Turtle Hill.
It really depends what kind of food you want, because there are tons of restaurants. I suggest checking out yelp.com to see what places are popular.
If you want Mexican/South American food and don't mind seeing hipsters riding around on fixed gear bikes, then there's the Mission. It's a nice place, a good cross section of people. There are places all over mission/valencia, from 16th street all the way down to the 20's. For burritos I like Pancho Villa, my girlfriend likes La Taqueria.
The Castro is actually a nice place to visit. There are lots of restaurants and shops. Believe it or not, there are non-gay bars in the area. My girlfriend's favorite place is Fuzio.
Walking Chinatown is pretty fun, although I haven't done it since buying bricks of fireworks in 1994 before the police crackdown on that open air market.
J-town is pretty cool, too. It's worth checking out. There's a good crepe place in there and many, many shops and restaurants.
The DeYoung and recently opened Steinhart aquarium are on the opposite side of town, near the beach. They are very popular. There is Beach Chalet in the area, which is pretty good. I prefer Park Chalet (which is downstairs) because it's cheaper for smaller portions.
You might want to check out Twin Peaks, it's one of the best views of the city. You can see right down Market to the ferry building. I like it better at night, but it gets cold out there. The drive up and down is fun, too. If you go there, drive down upper Market, the view is also great. And the road is a fun drive.
North Beach is lots of fun (Columbus St.). It's more known for the bar scene, but there are tons of restaurants. You can pick one at random and it'll be good. I like the stinking rose, but you have to 1) really, really like garlic and 2) not mind reeking afterwards. Broadway (strip clubs, etc) is just down the street.
Cow Hollow/Marina has a bunch of restaurants like Betelnut and A16, but I'm not a fan of the area, I think it's a little uppity (I worked down there for almost 5 years). It's one of the more homogenous areas of the city. The Marina Green and Wave Organ are a nice place on sunny days. The Exploratorium is also lots of fun, you could spend a day in there.
If you don't know where you're going, I'd avoid the Tenderloin, although there are a bunch of good restaurants there. And bums, drug dealers and tranny hookers. Like Dave Chappelle said: "ain't nothin' tender about it." One of my favorites, A la Turca (Turkish) is there.
I grew up eating on Clement. It's a nice area with lots of shops and restaurants. That's where I get my dim sum.
The Haight is always fun. There are a billion shops and places to eat. Upper Haight (near the park) is the main area. I like the bars in Lower Haight, but there aren't as many shops and restaurants down there, so I'd stick to Upper Haight. Outside UN Plaza in the Tenderloin, the Haight is bum central.
If you have tons to spend, I like the Slanted Door and House of Prime rib. Slanted Door is vietnamese fusion. It's in the ferry building (so is Hog Island Oysters). House of Prime Rib is on Van Ness nearish to the wharf.
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