New York analogy, FWIW: $1500 might be a fair estimate for finding a place in Manhattan with one or two roommates, but it's definitely possible to find a place in Brooklyn for $700-800/month if you share with several people (decent neighborhood, maybe 30 min commute to downtown) and $900-1000 for a place in a great neighborhood in Brooklyn in an even more central location.
Of course it will take quite a bit of Craigslist searching to find a good deal, but it depends heavily on both how much you're willing to compromise on distance from city center (some places on the periphery can be quite nice, and commuting via public transit = time to read so usually not bad) and # of people you share a place with.
Again I'm not sure how the intricacies of SF's real estate market compare to those of NYC, but just want to throw it our there that for someone young who's willing to live with others, it's pretty easy to find a place for well under $1,000 in notoriously expensive NYC, so I'd expect the same to be possible in SF, though I could be wrong.
I assume salaries are priced accordingly? You must be making 6000$/month at those rent costs.