"Hey! Good morning, Monstropolis. It's now five after the hour of 6:00 A.M. in the big monster city. Temperature's a balmy 65 degrees - which is good news for you reptiles - and it looks like it's going to be a perfect day to maybe, hey, just lie in bed, sleep in, or simply... work out that flab that's hanging over the bed! Get up, Sulley!"
Monstropolis could possibly be named after the real life city of Minneapolis, or possibly the term "Metropolis".
According to a DVD bonus feature "History of the Monster World", Monstropolis was founded after all of the monsters (originally a race of creatures called Mons), who once co-existed with humans, were all chased off the mainland, and eventually moved to an island in an unknown part of the world (which Monstropolis is implied to be located) where they have lived ever since and evolved into monsters by eating the strange fruit on the island (possibly the fruit sold at Tony's Grossery), and that the only way for them to enter human-inhabited areas was via closet doors.
In the original U.S. version, all crosswalk signals in Monstropolis read "Don't Stalk" and "Stalk" instead of "Don't Walk" and "Walk", respectively, but in the international releases, the crosswalk signals instead showed a four-clawed hand spread out for "Don't Stalk", and a two-headed monster walking for "Stalk".
Originally, Monstropolis was going to look more like a spooky Tim Burton-like world much akin to Halloween Town from The Nightmare Before Christmas, but after the realization that the monsters in this film scare because it's their main source of energy in their world rather than as natural behavior, the entire city was instead designed to resemble architecture of buildings in the early 1960s, representing the energy boom in the United States during that decade, and the significance is even important to the plot as there is an energy crisis plaguing Monstropolis caused by the children's growing immunity to being frightened by monsters.