Translation:Hello, do you have a room for two people?
Dictionary hint suggests "some", but my answer was rejected because it expected "do you have any room" instead of "do you have some room".
The hints will frequently contain valid translations of that word, which however may not be applicable to the current sentence.
In English I believe it is common to ask "do you have any rooms..." instead of "do you have a room."
It may be worth considering that as a valid translation.
I'm on the fence about this one, because the Czech sentence specifically uses pokoj, which is singluar. On the other hand, if we want to use "any" (which is accepted) then I'd say that "any rooms" is better than "any room." If we say, "Do you have any room for two people," it can be understood, at least in the US, to mean something general like "Do you have any place at all to put two people," which isn't quite the same thing, though it's very close. But I will add "any rooms" if the CZ natives on team feel the sentence supports it.
The word "nejaky" means "some kind of" so the translation should include it. "Good day, do you have some kind of room for two people?" or do you just omit it in Czech?
Here's my take on this. I'm not a Czech native speaker, but it's my understanding that nějaký is often used simply to mean "a/an," though it can also have the meaning that you suggest. On the English side, I'd say that "Do you have a room..." is much more likely to be used than "Do you have some kind of room..." -- maybe especially so here, since the sentence specifies the kind of room -- "for two people" -- that's of interest. (Just one person's opinion...)