I barely go into SF from Oakland except for college art projects or some weekends, so sorry if this sounds flowery.
There's plenty of art museums here, I can tell you that. In fact, most of them have free admission on one day of each first week of the month, and if you're into art the stuff there is worth the visit. One big one is in the middle of Golden Gate park, which has a beautiful Japanese garden and is also pretty nice.
Pier 39 and Alcatraz are touristy places, but they're still worth visiting. Union Square's got tons of shops and restaurants, so long as you don't stray too far to the West. Civic Center's where you can see the City hall, and while there's not much the dome is a piece of art in itself. Plus, there's a large patch of grass in the square right in front of the building where I spent some time chill out on.
Avoid the Tenderloin district if you can during the day, but especially during the night. What is the Tenderloin? Imagine a miniature Gotham City restricted to several city blocks west of Union Square, and east of Civic Center north of Market Street; except that there's not a single Batman in sight. The same goes with the Mission district. The city's also got a large homeless population, and while most of them are friendly just be cautious who you come across in these parts.
There's a nature trail at 'land's end' on the west of SF, and it runs along a cliffside with a very sweet view of the Golden Gate Bridge and the opening into the Bay. It's also right near the Legion of Honor art museum.
Right across the bridge, there's also a small neighborhood called Sausalito. I had lunch there once, and it's worth a walk around.
Also, if you're ever going to visit SF, wear a jacket because it's VERY windy. I didn't think it could be so chilly in California in the middle of summer, but San Francisco proved me wrong.
SF's a great city; definitely worth at least one visit.