Clubs de alterne are in effect brothels, but they shouldn't be called that here, because "alterne" is being distinguished from "prostitución" (as Carol rightly says). Prostitution is legal in Spain but pimping is not. "Alterne", however, is, because formally they are not brothels, even though they serve the same purpose. Their legal fig leaf is that in theory "alterne" is not inevitably and by definition for paid sex. It is ostensibly more respectable than that.

Alterne is defined in case law as "la captación de clientes varones, mediante el atractivo sexual al objeto de que consuman bebidas". It's understood that the captación is normally for sex as well as drinking. Nevertheless, it gives alterne clubs a distinctive nature for which we need a distinctive name.

I think that since what happens (as I understand it) is that when a man enters an alterne club he will shortly be joined by an accommodating young woman, drinks will be ordered and they will normally retire to a room in due course, a suitable term would be "escort club". There is something euphemistic about the word "alterne" and it would be good to capture that in the translation. "Gentlemen's clubs" is too euphemistic, to my mind (it makes me think of Pall Mall and Bertie Wooster); "sleaze clubs" is accurate, in a sense, but the wrong register (the very opposite of euphemistic). But "escort" captures the verbal fig leaf of the Spanish term for me.

Here is a website for a club called Perla Negra in Barcelona (don't open it if you're easily offended), which calls itself an "escort club" and even at one point an "escort brothel". It features an "escort bar" as well as rooms rentable by the hour. I would say it is an alterne club:
http://www.perlanegrabcn.com/en/escort-club-facilities/

Alterne places are (or at least were) colloquially known as "puticlubs".

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Note added at 12 hrs (2016-03-03 08:48:36 GMT)
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David's "hostess" is an excellent option. I am a bit torn as to which is better. On the one hand, "escort" is commonly used as a euphemism for a prostitute, and in this context it doesn't necessarily have the usual implications of accompanying someone to social events. Of course it can; "escorts" can be paid companions who are sometimes (tacitly) expected to sleep with the client afterwards. But in the context of "escort club" it just means having a drink with them and then going to bed with them; if you go to an escort club you're not expecting the "escorts" to leave the club with you; your business is conducted on the premises.

"Hostess", on the other hand, is the word for a woman whose job is to dance or drink with customers in a nightclub. It doesn't necessarily imply prostitution, though of course it can and often will.

So I would say that "hostess bar" is more euphemistic and less clearly a brothel than "escort bar". I think you might genuinely visit a "hostess bar" without getting laid or intending to; it's very unlikely you'd visit an "escort bar" for any other purpose. I would say the latter is true of a "club de alterne" as well, and yet if you needed a term for a "hostess club/bar" in Spanish, that's probably what you would call it, and in theory "alterne" doesn't have to be sex. So I believe you could argue this one either way.

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Note added at 12 hrs (2016-03-03 09:12:29 GMT)
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"Escort bar" seems to be a favoured term in Barcelona. Here's another one. When it says you can indulge in a drink or two "either before or after the meeting with your escort", it means before or after sex, of course.
http://www.lavieenrose.es/en/bar-escorts/

"Amsterdam
Can anyone recommend a good "escort bar"?
Will be visiting soon, and as much as I'd enjoy giving the red light district a try, I know I will be wanting something more intimate.
I've heard there are some bars that also double as escort places?"
https://www.reddit.com/r/Amsterdam/comments/30svfi/can_anyon...

While "escort clubs" are very thinly disguised brothels, "hostess club" is a good deal less sleazy, largely because it is strongly associated with the Japanese "hostess" phenomenon. These are definitely not brothels at all and there is no expectation of sex on the premises, though there can be on subsequent "paid dates". On the other hand, though someone visiting a "hostess club" in Spain would probably not expect it to be like that.
https://en.wikipedia.org/wiki/Host_and_hostess_clubs

So it's a question of how clear you want the prostitution element to be.

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Note added at 1 day1 hr (2016-03-03 22:21:29 GMT) Post-grading
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Thank you, Richard. I am going to put "hostess" in the glossary entry as well; I hope that's all right with you. "Hostess" is closer to what alterne is supposed to be (and perhaps once was); "escort" is closer to what it actually is in practice. I think users will find both terms helpful.