I have been a few times so not an expert but what I have gleaned so far:
Blair street I've been to most often. It's good and central, always been a positive vibe from receptionist. The changing area is totally communal so often see other punters. I've gone a few times and always enjoyed myself. The attitude of the girls in the "choosing room" varies, sometimes the mood is a bit low
London street I went to once and it was a good punt, you walk straight into the "choosing room" and the girls seemed, on this occasion at least, to have a better vibe than Blair street. There are changing cubicles so little more private, but still quite possible to bumping into other punters
New town sauna I went to once and they totally dicked me around with swapping out a slender girl I wanted for a fat girl. It was a one off, so maybe I was unlucky or maybe they are always a bit shit.
Girls wise, I wouldn't say the choice of girls of amazing and there is a fair turnover too, so I wouldn't like to predict one place will necessarily be better than another. You can always call ahead and ask for a rundown of the girls and what they are like and you'll get an age/build/nationality summary. If you've been punting in London then I'd lower your expectations.
Timing wise, everywhere in Edinburgh is busy right now. Even before the fringe, I went into Blair street at the back of 10 one morning, not long after it opened, and it the choice was one girl! All others were busy.