"come down to the room" = 93.3m hits on google. "come down into the room" = 7.1m hits on google. Both are correct and both should be accepted but clearly the former is a more common way to describe this movement.
As awkward as they are, I prefer the more literal English translations, especially if I'm translating into Hungarian. But I think both the more natural and the more literal English translations should be accepted when translating from Hungarian.