Earlier quoted context omitted.
$3k per month should get you a studio apartment in the Mission, SOMA, downtown etc. If you're willing to share you can get for cheaper. If you want 1 bedroom you're going to struggle to find something for $3k.
Less 3k a month is in solid 1 bedroom territory for those neighborhoods these days. Around ~$2700 is what I'm seeing in my search for decent 1bedrooms in good SF neighborhoods.
From what I have seen the salary spread between say SF and NYC is not enough to compensate for the higher rental costs in SF.