I have this question: Do I only have to use "at" in the following sentences or is it also possible to use "in"?

1) I can buy books at the bookshop. / I can dance at the disco./ I can stay at the hotel.

2) What about the shops which contain an apostrophy? - I can buy meat at the butcher´s./ I can buy milk at the dairy´s. (Can I say "buy meat/milk "in" the butcher´s/dairy´s"?

(I am sure it is possible to use: eat at/in a restaurant (English Grammar in Use by Murphy - (at versus in), page 248, Cambridge University Press 1985, 1994).)

Bye Mowgli
Yes, you can use at/in in all those cases, Mowgli.
"in" is always more specific than "at".
If you are really physically located within the walls of the library as you read, then both "in" and "at" will do.
If you are in the habit of reading books just outside the library, in a little garden or park beside the library, but still on the property associated with the library, then only "at" will do.

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Hello Mowgli,

"at" is preferable here. "In" is not wrong as such, and would be understood, but it's not the normal word in this context.

nb, you shouldn't use an apostrophe with dairy. It can be used with butcher - to impy it's the shop ran or owned by the butcher him/herself, but it's simpler just to say "Can I buy milk/meat at the butcher". You can't use it with "dairy" - it implies the establishment belongs to the dairy, whereas in fact it is a dairy.
Following this subject. What would be the proper use in this sentence?

I like reading books in/at the library.
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 CalifJim's reply was promoted to an answer.