Translation:Please wait in the hallway.
下 isn't specifically "down". In the case of the word corridor or hallway, it probably means "under, below, beneath".
廊下 (ろうか) "corridor, hallway, passageway".
- 廊 (ろう) "corridor"...
- 下 (か) "down, under, below, beneath, descend, inferior"
廊下 is a corridor inside a building — a corridor(廊) under(下) a roof.
Another kind of corridor is written in kanji as 廊架 and is pronounced ろうか too. The different kanji 架 (か) means "frame" (such as a wooden frame).
If you look up "廊下" and "廊架" with Google's image search, you'll see the difference between these two types of ろうか. The images for 廊下 will virtually all be of hallways inside buildings where they are under proper roofs, whereas the images for 廊架 are rather different to this. ^^
From what I understand, "at" is a simple location marker while "in" describes a relationship between the subjects when talking about locations and stuff.
"He is at the door" (the man is located at the door)
"He is in front of the door" (the man is located to the front of the door/the relation between the man and the door is that he is in front of it/the man is at the door's front)