Rescue Beauty Lounge and Bliss also have LA locations.
I'm a regular at the Bliss in LA (mostly because I live within walking distance!) so I'd probably go with Bliss.
I don't know if this will sway you, but if you go to the Bliss on 57th, you'll be basically across the street from Henri Bendel and Bergdorf Goodman. The Soho one looks like it's going through renovations so you wouldn't get a locker, which sounds like a PITA to me.