Where is the endless staircase in super Mario 63

The endless staircase is through a door in the Star Room, which is accessible from the Upper Hallway. Note that you need the Red Shine Sprite to get into the Star Room. There is also a shortcut to the staircase from the Main Hall. Just stand on the platform under the huge sun on the wall, then use Rocket FLUDD to blast up through the ceiling. (Rocket FLUDD is hidden in a secret room in the castle.)