First of all, I have never been to any of these places.
They are called 出会い喫茶 (であいきっさ Deai Kissa) or 出会いカフェ (であいかふぇ Deai Cafe).
They are all the rage nowadays and there are some even in the rural areas like where I live.
Even though any "real action" takes place OUTSIDE these places, it is prostitution when you think about it. The big difference is in a Deai Kissa, it is the WOMEN who is in control.
For men, these establishments are attractive because they are more casual ,not to mention legal, compared to paying for a professional's services.
Cheaper, too. Or so I hear.
As for the documentary film you are looking for, I have no idea what it is called. Was it indeed a feature film or a segment aired as a part of a News show?