Really? It's surely not what I would say. My personal conjugation is something like this:

A: Do you like the hotel you are staying at?

B: A asked him if he liked the hotel he was staying at.

A: Did you like the hotel that you stayed at?

B. A asked him if he liked the hotel that he stayed at.

A: Have you ever liked any hotel you stayed at?

B: A asked him if he had ever liked any hotel he stayed at.

Maybe it's not what someone should write on an English grammar test (I really don't know), but that's the way I speak. (And write, for that matter.)

He asked him if he had liked the hotel

I think that's a matter of context. #3 is correct if the person being asked was staying at the hotel at the time when s/he was being asked, but the OP and #1 are correct if the person had been staying there in the past, or prior to being asked.