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Which word would you use in this question, which or what?

At which hotel will we be staying during the conference?

At what hotel will we be staying during the conference?

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The first link provided by Choster in the Comment section above has good answers to a similar question. I am adding this answer here because it quotes from a relevant source.

The source is The Cambridge Grammar of English (p388) which states the following (slightly adapted here):

What is used when specific information is requested from a general or open-ended possible range. Which is used when specific information is requested from a restricted range of possibilities:

  • What's your phone number? [*Which is your phone number?]

  • Looking at a pile of coats: Which is your coat? [*What is your coat?]

On this basis At which hotel will we be staying during the conference? would be the usual choice here.

However, the book goes on to state:

Where the number of options is shared common knowledge among speakers and listeners, what + noun is often used in informal contexts. Here, what is an interrogative pronoun used as a determiner:

  • What side of the street is the shop on?

  • Did you see the documentary? - No, what channel was it on?

So, in summary both questions are possible but At what hotel ... ? is probably best restricted to informal contexts.


Addendum

In fact, starting with the preposition in itself makes the question more formal than pushing it to the end: What hotel will we be staying at? So, At what hotel ... ? is somewhat of a mixture of formal and informal, and probably best avoided for that reason alone.

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‘Which’ and ‘what’ are both heard in English in this context.

‘What’ is marked as being more colloquial, whereas ‘which’ can be seen as anything from neutral to formal in style.

So if you are writing a more or less formal (or at least not informal) message to ask where you will be staying, ‘which’ is most likely to be the better choice. If you are simply talking to someone you know well, ‘what’ may sound more natural.

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  • Welcome Janus, I'm pleased to see you on ELL! – user114 Aug 2 '13 at 14:25
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When there are several hotels for the questioner to chose, he will use "which", while when he does not want to choose or has no choice of the hotel and just want to know the name of the hotel that he will live in, he will use the word "what".

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