There are two restrooms in Yume Nikki, found in Block World and Graffiti World. Using a restroom doesn't do anything except allow the player to hear a flushing noise when Madotsuki uses it.
Restrooms
The two restrooms in the dream world are located in Block World and Graffiti World, both of which can be accessed from the Nexus. There is one male restroom and one female restroom, though Madotsuki can enter both of them regardless of which gender they are meant for. Entering a restroom will simply play a small flushing sound after a short time and Madotsuki will emerge after the noise plays, closing the door behind her. They do not do anything beyond this.
If the Bicycle, Severed Head, or Umbrella effects are equipped, the restrooms can not be entered.
Block World
The male restroom, which is primarily blue, can be found in Block World. It can be found southeast of the Nexus entrance. Despite being a male restroom, Madotsuki is still able to enter and use it.
Graffiti World
The female restroom, which is primarily pink, can be found in Graffiti World. It can be found south of the Nexus entrance, located at the end of a path that appears to be the tail of a large graffiti creature. Once again, Madotsuki uses it like normal.
Theories
In the game, Madotsuki can use both male and female restrooms. This has led to claims that Madotsuki may be non-binary. There is also the theory that she may be transgender, and the fact she can enter both restrooms is simply a memory of the past (before transitioning) and present (after transitioning). Other aspects of the game may hint at some confusion of gender identity, such as Closet Madotsuki, and how various characters such as KyuuKyuu-kun and the Floyag resemble reproductive organs.