"Where is your room?"
Translation:Wo ist dein Zimmer?
They have a difference in meaning. Zimmer is a private room that belongs to someone, it implies that the room is filled with private stuff of the owner. It's like the 'home room inside the house'.
Raum means a room in general (it can also mean space in other contexts). The term implies that the room has another purpose than a purely private Zimmer, like the kitchen, buro, bathroom, conference room, and so on.
There is also the term die Stube which can mean the living room or the private rooms in barracks.