I think you'd be rather happy in the SOMA area (south of market).

It's a mixed use industrial/residential area, that is the heart of the club district in SF. There's alot of newer live/work lofts popping up, that can be fun to live in, and when SF has wearhouse parties, that's where they are (although SF has very few of those lately... most are in the east bay). It is about as safe as an inner city can be, plenty of stores and shopping and public transportation, so you won't need a car. Pretty busy in the daytime, but rather quiet at night (plenty of parking at night too!)

If you look at a map of SF, it would be everything between market street and Townsend, between the Embarcadero and the 101 freeway. The most expensive areas are definetly closer to the bay (it's all new construction there). Places to avoid would be anything within 1 block of 6th street and Mission.

Other than that, the other area I think is safe and desireable, is an ambigous area with no name. It's between the Castro (the gay district) and the Mission (latino district). Looking at a map, it would be anything just off of Guerrero & Deloris, between Market & Cesar Chavez. Lots of old Victorians that have been cut into flats, and alot of younger/hip people like to live there in shared units. Public transit, shopping, safe, cool people. Everything you could want except for parking.

As for specifically. Check out craigslist.org for listings.