Hard to pin any one thing down in sf because there are so many options. If you really want to avoid tourist traps then you may want to steer clear of the wharf and north beach.
If you are a wanna be hipster then you have to do the mission circuit like me:
La Palma mexicatessen for some badass tacos
Humphrey slocombe for weird ice cream
Ritual for coffee
And dynamo's for donuts.
Arinell's if you like pizza.
As far as lesser known stuff, a real gem is the northwest corner of sf, to the west of gg bridge. Thereis a beautiful hiking / jogging route at the park near the legion of honor that overlooks the ocean - simply amazing if you're lucky and its a clear day. The Asian food in west sf (outer Richmond) is also far superior to most of the garbage you get in Chinatown, and way cheaper.
If you have any other specific questions let me know, there's too much to post about. I live in soma myself and its also got a lot of good places to eat and drink , the city is pretty packed with good stuff given its small size.
You'd be a moron to spend any more time in San Jose than it takes to drive past or get a train out of.