word choice - Can I say "Where can I find 'a' post office"?

It's a question in a grammar app.
"Where can I find _ post office please?".
I chose "a", but it says "the" is the correct answer.
Same problem with this question:
"Let's go to _ cinema tonight."
I know the answer is "the", but I don't know why "Let's go to a cinema" is wrong.

I thought when you specific mean which cinema or which post office you should use "the", otherwise "a/an" is also okay.

Could someone please help me?

Answer

Go to the — is idiomatic English used even in cases where the speaker isn't referring to a specific (definite) location, but rather seeking a specific kind of service or business. For example, we go to the post office, the hospital, the store, the hairdresser, and so forth. You can think of it as a kind of metonymy where “go to the store” means “go shopping” and “go to the barber” means “get my haircut.”

The same idea applies to similar constructions like “Where is the post office?” Following the same logic as above, this roughly means, “Where can I post my mail?” Likewise, “Where is the bathroom?” asks “Where can I use a bathroom?” (You could also parse this as “Where is the [nearest] post office?” but I think the idiomatic explanation is a better fit.)

Note that a native speaker would find the question “Where can I find a post office?” entirely natural, and in some cases might even prefer it. Thus, your answer to the grammar quiz wasn’t incorrect, strictly speaking. However, quizzes like that typically ask for the “best” answer, and in this case “best” likely means using the “go to the —” idiom.