Learn Polish: Jaki napój lubisz? - What drink do you like?

In English, we say "What drink," but in Polish, when "what" is attached to a noun to ask about its type or qualities, you must use jaki (which literally means "what kind of" or "which"). You only use co when "what" stands entirely on its own as a pronoun, like in Co to jest? (What is this?).

Since napój is the direct object being liked, shouldn't it be in the accusative case?

It is in the accusative case! The verb lubić (to like) always takes the accusative. However, napój is a masculine inanimate noun (a masculine word for a non-living thing). In Polish, the accusative form for masculine inanimate nouns looks exactly the same as their basic dictionary form (the nominative case).

Does Jaki also stay in its basic dictionary form here, even though it is part of the direct object?

Yes. Because jaki acts like an adjective describing the masculine inanimate noun napój, it follows the exact same rule. It stays as jaki in the accusative case. If you were asking about a living masculine noun instead, both words would change their endings, for example: Jakiego psa lubisz? (What dog do you like?).