As other's have said, there is a wide variation in what the States are like depending on location. And if you were a white British guy with a London accent, I would say you would be well received almost anywhere you go (some exceptions because some US-born & -raised folks are just assholes to foreigners).

BUT! I worry that a Black lesbian foreigner would get the short end of the stick in too many ways. You'd be safest in big cities, but that drives up your cost of living; college towns would be a cheaper and almost as safe second, but US colleges are entering a crisis as the enrollment reaches a demographic cliff that will cause many institutions to close in the coming decade, taking down their towns with them.

When I saw your title my first reaction was, "How cool! I hope she [I assumed you had found the Perfect Woman] works out!" Then I found you had more mercenary motives (nothing wrong with that!). If you have a good friend/potential significant other in the States who can take you over the cultural bumps and provide some occasional other assistance, I would be much more positive about your chances, dear lady, but as it is, I agree with most of the responses that now is NOT a good time to emigrate to our country.

I don't know enough about Australia to suggest it as an alternative, other than, yes, everything I've read says the wildlife will try to kill you. 😉

Good luck, Natalie!