Learn Russian: У вас есть какие-нибудь интересные книги?

какие by itself is a question word meaning "which" or "what kind of". By adding the suffix -нибудь, it changes to mean "any (kind of)" or "some (kind of)". We use it here because you are asking if they have any interesting books at all, without looking for a specific one.

Why is it spelled какие-нибудь and not какой-нибудь?

The first half of the word acts just like an adjective, so it has to match the noun it describes. Since книги (books) is plural, какой changes to its plural form какие. The -нибудь part always stays exactly the same.

Could I use какие-то in this sentence instead?

It would sound unnatural here. As a general rule, use -нибудь in questions, requests, or future tense when you don't know if the object even exists yet. Use -то (like какие-то) in statements when you know a thing exists, but you just aren't sure exactly which one it is.

A quick refresher: why do we say У вас есть to mean "Do you have"?

Russian rarely uses a direct verb for "to have". Instead, it uses this structure: У (at/by) + the owner in the Genitive case (вас) + есть (is/exists). Literally, you are asking: "At you, do there exist any interesting books?"