The Nexus is a single room, with thirteen doors leading to the different areas in the dream world. The Nexus is found beyond the door that is in Madotsuki's dream room, but can be reached by pressing 1 with the Medamaude effect while still in a dream area (or alternatively, reached by going back through the door that you came in). Eggs can be dropped here by equipping an effect and pushing 5.
There are 13 doors in the Nexus in total. The top one leads back to Madotsuki's Room, and the other 12 respectively lead into the original locations: (counterclockwise from the top) the Forest World, the Block World, the Puddle World, the Dark World, the Snow World, the Mural World, the Graffiti World, the Eyeball World, the Candle World, the Neon World, and the Number World.
Some locations cannot be reached directly from the Nexus. These have to be found by exploring the original locations, or by talking to the Hat-and-scarf girl.