I always go to bars in the SOMA district since that's where most of my friends in the city live, but I'd like to branch out!
Here are some good ones:
Mentioned in this answer:
My friends just opened Reed & Greenough Distillery in the Marina. According to the press, it's "upscale cocktail sanctuary inspired by a sign looted during the 1906 quake and stocked with all the classic underpinnings of a swank Pacific Heights mansion game room." You can read more about it here.
The Mission area has some great bars - including Make-Out Room on Mission St. Fun vibe and always intersting people but very safe and well priced.