Corrected entry: In season 1, episode 7 (Kiss and Tell), Lorelei tells Rory to go to the bathroom so it won't look like they were coming back to the living room (where Dean was) together. Rory opens the door in the small hallway leading from the kitchen to the living room and goes in. We assume it's the bathroom. Then in this episode, Rory tells Lorelei to get rid of a box in which she had put all of the things that reminded her of Dean. Lorelei agrees but when she leaves Rory's room she goes to the same place in the hallway where the bathroom presumably was and opens the door to reveal a coat closet, not a bathroom. It's the only door there. This space is confirmed as the coat closet in "Love, Daisies and Troubadours" when Rory finds the Dean box. (00:39:00)
Correction: There has been other references to the downstairs bathroom throughout the seasons but then yes it somehow turned into the coat closet, and I couldn't find any other logical place it could be.
Correction: So Rory didn't go to the bathroom. She honored the spirit of her mother's request by hiding and not returning to the living room at the same time as her, but saw no reason to go all the way to the bathroom for no real reason.
Phixius ★
It is possible that Rory was hiding in a closet; however, in later episodes, they do reference a downstairs bathroom. Luke asks Kirk why he won't use the downstairs bathroom and Kirk says that the tile on the downstairs bathroom hurts his knees.
Sookie went into the infamous closet/bathroom and referred to it as a bathroom asking if "the silver bottle on the sink is soap".