From the Super Mario Wiki
Dome Castle is the place of residence to Mario, Luigi, Princess Toadstool and Yoshi in the Super Mario World cartoon. The Dome Castle, like the rest of the buildings in Dome City is not actually a castle. It looks like a simple dome with windows and a door carved into it. Surrounding the Dome Castle is a water-filled moat; the Dome Castle also has a vine growing across the side of it.
In the episode "Born to Ride", Mario and Luigi, after some effort, managed to install a bamboo piping-system and sink in the Dome Castle. Oddly, the Dome Castle looks larger on the inside than on the outside, having multiple rooms and a staircase.