Ness's level takes place in Onett. This was created before I even saw his new stage for Melee. You can climb up the fire escape or the circling platforms at Ness's house. The only way to lose a life in this course is to be tossed far off the screen or being hit upward.
Peach's stage is in the first room of her castle. You can pretty much climb on anything that has "lines". The only way to lose in this arena is to be tossed out.
Bowser's stage is in his old-school castle from the NES. The two floating platforms go all across the screen, so your not always safe when the bridge is gone. The thromp in the background is just background design and nothing else. In this stage you can lose a life by falling in the lava, tossed off the screen and surprisingly hit upward, out of the ring, breaking through part of the ceiling leaving an opening. If the ceiling isn't cracked you lucked out and are saved.
Pit's level is basically on a platform with Greek ruins and architecture. It was an idea from a level from Melee that gave me the idea. That level was rumored Pit's, but then made official being a Zelda characters, by a triforce marked on a step. You can climb on almost anything. I call the two story high pillars the colleseum, although it bears no resemblence. You can lose a life everyway in this stage: up, down, left and right.