The original design for the Junkyard has a car with a visible number plate (TSE 1 in the video, or NAP+number), an oven, a pipe (where Mistoffelees notably conjures Old Deuteronomy from). The area is strewn with trash, all familiar products scaled 4x larger than reality. The sky has a moon in the background. For more information about the various sets, see Here.
Throughout the show we remain in the same space; the characters come and go. The only time the space is transformed to lead the audience somewhere else is during Gus' dream sequence, "Growltiger's Last Stand". Then, dependant on production, we either see his dream in which a lavishly detailed pirate ship appears, or we see the Cats re-creating the scene for him from the surrounding junk.
Non-replica productions have set the show in other locations, such as an attic, or an abandoned travelling fair.