I would not move across country without a firm job that can cover your expenses. Especially if you have no social network to support you. This is how lots of people become homeless.
So start there, look at where you can find work, maybe make some phone calls, send emails, etc. Then once you have a sense of how much you’ll be able to make you can look at what housing is available to you. But realistically, surviving in expensive places with the amount of money you currently make may be quite difficult. Keep in mind that many of the very lowest cost apartments you see may be scams.
Also, consider looking at some cities closer to home. There may be some pockets of lgbt friendliness in your region that you aren’t considering and they may be lower cost of living. The places you listed are all extremely expensive and not necessarily somewhere you can just move without a plan.
I know everyone hates Reddit here but once you start to narrow things down, it might be helpful to ask specific questions on local subreddits to get input from locals.