Best placed in the ವಾಯವ್ಯ
The north-west is the classical bathroom corner: the direction of movement and of things that pass through, which is exactly what a bathroom is.
What the ವಾಯವ್ಯ governs
The north-west — Vayavya — is the air corner: movement, circulation, things that come and go. Guests, storage in transit and utilities sit here easily, and nothing meant to be permanent does.
Where the ಸ್ನಾನಘರ belongs
Bathrooms and toilets are the rooms the tradition most wants kept away from the protected corners — not because of the compass alone but because of water, waste and the drainage that follows them. Where they cannot be moved, the remedies are about containment.