Congratulations Anna on that first step! After almost 9 months of HRT, I have been out in public about a dozen times. Most of those have been to trans friendly clubs, although I have been to my therapist a few times that way.
But not long ago, I visited a hospital emergency room at about 4am, after being out at a club. My sister had taken her fiancee there, after he had become violently sick, and I wanted to keep her company. It was an interesting experience which I would tell here, but I don't want to steal your thread.
By they way, I don't believe now that my transition really began with me starting HRT. I see the real beginning as happening the first time I ever stepped out of the house dressed as a female. I knew that if I ever got the courage to do that, my life would never be the same. I did it at night, and I live in a really dark neighborhood, so there was little risk of anybody seeing me. But my heart just pounded when I took that first step out the door.