I'm not sure what kind of work you're interested in, but the way that the Bay Area used to be, in the early 1970's (ancient history!) was that it was the heaviest unionized area in the country. You cannot be turned down because you aren't a union member, but you can be required to join the union after a probationary period. Jobs have to be offered to unemployed union members before the position can be made open to the general public.
You may find it easier to find a job in Oakland. The cost of housing is also more affordable, and if you have a car, or if you use public transportation, San Francisco is still convenient. Next to Oakland is Berkeley, which is a very desirable place to live, although it also can be a bit pricey as well. It's a college town, University of California, Berkeley. It's the home of a lot of the history of the late '60's. People's Park, Mario Savio, free speech. You may still be able to find affordable housing on the western side of San Pablo Avenue, and It's a fast and easy commute to either San Fran or Oakland.
San Francisco is well known for its' generally accepting attitude towards "alternative lifestyles," whether that means being part of th LGBT community, or independently gender or sexually variant. I found SF to be as accepting, in those years, as I could hope for. Berkeley was good also. I used to hang out on Telegraph Avenue in Berkeley. This was 1969-1971. I'd be standing in front of Moe's books with my friends, with my hair nicely done, maybe a touch of makeup, and the cutest brown suede mini-skirt that I have ever worn! One afternoon, the police drove up, and asked me to "Please!!!" get into the car.. They drove me around the corner and pulled over. They then took a few minutes to explain to me that they knew that I was a male who looked like an attracive young lady, but that not everyone would be able to tell. This is when they spent the time to explain to me that there was a very serious problem with RAPE in both San Francisco and Berkeley as well, and that I should be very aware of what I was doing, and that I was vulnerable. I only weighed about 115 pounds, and if anyone ever assaulted me, I'd really be in trouble. I sincerely appreciated the interest shown by those members of the Berkeley Police. Yes, I was more careful after that discussion.
I truly wish that everything works out for you!!! I lived in Berkeley for over two years and loved it! The Bay Area has, in my opinion, the best climate in the country, and the life style is far more relaxed than the "State to the South" southern California. The negative part, is that San Francisco has the most expensive real estate in the country, and that it can be hard to earn a living.
I really wish that I could afford to live there!