Okay, so I think I may as well post this now so that everyone can contribute. This is what Psychic Politoed and I have compiled from reading this thread, and Psychic Politoed from reading some threads on Smogon.
Each Pokemon type and where they send you:
Pleasant Forest: Grass, Electric, Poison, Bug
Rugged Mountain: Fire, Rock, Ground
Spooky Manor: Psychic, Ghost, Dark
Sparkling Sea: Water
Icy Cave: Ice
Windswept Sky: Flying
No preference: Dragon, Normal
Not Tested: Fighting, Steel
Dual types will take you equally to both preferred places. For example, Gengar, which is Ghost and Poison, will take you 50% of the time to the Manor and 50% of the time to the Forest.
We do not yet know what happens if you have a dual No Preference/Preference type, such as Dragon/Dark (Hydregion) or Normal/Flying (Pidgeot, etc.).
So if anyone tucks in a Fighting-type, a Steel-type, or a dual No Preference/Preference type, please respond to this post and let us know what happens. Tell us who you tucked in, which areas you went to, and how many times you went there. If you believe any of these types/area preferences are mistaken, please respond and help us correct it so that Serebii users know who to tuck in to make their DW experience as enjoyable as possible!