Whenever Naruto sees the Kyuubi that Minato sealed inside him, we see this room with water on the floor and a big door behind which the Kyuubi stays. What is this place and where is it?
The place that we see is within Naruto's subconsciousness and its as a result of the Eight Tetragram pattern which is the sealing formula used by Minato to seal the Nine tails within Naruto.
According to the Wiki, When Naruto wants to speak to the Nine-Tails, he enters a subconscious plane that resembles an underground complex, with pipes running along the ceiling and various hallways. The floor is flooded with a shallow layer of water; the Nine-Tails' growing influence over Naruto is sometimes depicted as the water level rising.
The seal is an anchor that binds the two together. The Kyuubi in theory is a mass of chakra that was given sentience by the Sage of Six Paths. Fuinjutsu or the art of sealing allows them to seal them away. The Tailed beast exist in a sub-conscience as a by-product of the seal. Depending on the nature of the seal defines how they are locked up. Kushina is in a field with Kyuubi chained up while Naruto has it in a cage in a complex similar to a sewer. In theory, the Kyuubi exist in a sub-conscience while it's chakra is sealed aswell, slowly to merge with Naruto's. If your wondering about the shared space where they all meet, it is a result of the Sage's link he made when telling the Tailed Beast he's dying.
Add corrections if i'm wrong.