Below is a guide to every drop room in Mythic Nexus.
Each cave has THREE different fall rooms, not two. The third room is usually a rare fall, either because most people travel on certain tiles, or that it's not a very explored room.
Fall rooms marked with a * are 'rare' drop rooms.
Rabbit - Forage fields / *Rabbit leap / Rabbit hole
Monkey - Monkey wasteland / Monkey divide / *(unsure)
Dog - Run / Gnawed bones / *Mongrel gateway
Rooster - Chicken conquest / *(unsure) / Angry roost
Rat - None, you just walk in from sentry room!
Horse - Hooved sands / *(unsure) / Clovers
Ox - Sunset / Ox path / *(unsure)
Pig - Grub hunt / Boar fields / *Clove hill
Snake - Final Rest / *Snake sleep / Snake fields
Sheep - *Sheep bridge / *Sheep patrol / Shadow grove
Tiger - All over the place @_@ Varies per cave level
Dragon - Dragon death / *Dragon gold / Jeweled dragon