OP is mistaken even in supposing that the word country is "omitted" in the examples. That specific word never occurred earlier in the "conversation", and the second sentence could just as well have been Which place did he like best?, In which of those did he meet her? anyway.
But actually, there's no syntactic reason to identify any specific noun after which in such contexts. For example,...
We have red wine and white wine. Which do you prefer?
...is a perfectly natural construction, in both formal and informal contexts (informally, We've got... Which do you want? would be more common, but that's irrelevant to the point under consideration).
It might help to note that which is sometimes identified as an interrogative pronoun. That's to say, it's already a "nouny" sort of word anyway, so there's no reason to suppose grammar / syntax would require it always to be coupled to another noun. Of course, semantically it might be needed to clarify meaning / resolve ambiguity, but that clearly isn't the case with OP's examples.