actually i was having the same problem... OP, are you asking for playability... or collecting in a book. most of the answers given are for playability...
my Trainers book is divided by Supporters/Items/Stadiums... i personally go with if trainers name is in title, and picture, its a Supporter. If its and obvious place. its a stadium... actions and inanimate objects are items... but i'll admit im still iffy on a few.
Breeder Fields - (Breeder/Supporter) or (Fields/Stadium) or item?
Arcade game and Card-Flip game (game corner) - game/Item or game corner/Stadium?
Ruin Wall - Place or item? (you cant take it with you) probably (puzzle/item, since there are multiple Ruins/Stadiums)
there is a Pokemon Center 'stadium' building(labeled Stadium), Pokemon Center item (pic of Ball Healer Machine) but Night Pokemon Center is a building... so Stadium or Item?
-named Supporters - Protags, Gym leaders(not badge or stadium), Professors, Bill, Mary, Mr Fuji
-trainer class Supporters - Gambler, Lass, Breeder, Trader
-Supporters pic designated to a gym leader... otherwise would be an item(action) - Charity, Fervor, Good Manners, Secret Mission