I live and work in San Francisco so I could probably comment on your chances.
Yes, the entire San-Francisco Bay Area is a desirable destination for nurses because of the higher salaries here. However, the cost of living is up there (the city of San Francisco is next only to NYC as far as the costliest city to live in the US). Having said, that nothing stops nurses from other parts of the US (and Canada) in seeking opportunities here and that's OK by me - we all make our own choices in the end.
Those nurses who come in with a few years of experience usually have a better chance of getting jobs. The fresh grads, even those who went to California schools
, tend to wait the most to land a job. Many experienced, non-California nurses from somewhere else get in as a traveler. Hospitals here still use travelers and some travelers do end up getting hired by the facilities they once contract with.
The question is how do you start this process as a Canadian citizen knowing that you can't apply for an RN license in California without a valid US SSN? What some Canadian nurses have done in the past is to start in another state first (i.e., Washington, like you mentioned can be an option if they will let you take the NCLEX without a US SSN). Whatever you decide, good luck on your future career.