Easy, New York. If you're like me that's probably what you thought. In actuality the city Arnold lives in is actually fictional, like Gotham or Metropolis. That being said, it is based off very real cities in the US. Although it would be easy to assume it is based off the sprawling metropolises of Chicago and New York, the city actually drew inspiration from two West Coast cities.
Craig Bartlett (the show's creator) was born and raised in Seattle, Washington. Since it is relataviely near to Seattle, Bartlett also spent a great deal of time in Portland Oregon. Both of these beautifully, unique cities served as the inspiration for the city in Hey Arnold! It's only fitting that one of the best cartoon series from the 90s be set in a city based partly on Portland. The dream of the 90s is alive in Portland after all.
Here's another interesting fact about the show. Mr. Simmons, Arnold's super sensitive teacher is homosexual, according to Craig Bartlett. This fact is hinted at in the episode "Arnold's Thanksgiving." Arnold and Helga end up going to Mr. Simmons' house for Thanksgiving dinner. There they meet Mr. Simmons' mother and uncle as well as his friends Peter and Joy.
During the meal Simmons' mother says in a rude tone that she was not aware that Peter was going to be at the dinner, to which Peter replies, "There's a lot of things you don't know." Later she suggests that Mr. Simmons should take Joy to the ballet. When he remarks that he loves the ballet, Peter shoots him a nasty look, after which Mr. Simmons sheepishly retracts his statement. It has since been revealed that Mr. Simmons and Peter were involved in a secret romantic relationship. Just another example of very complicated themes being woven into an incredible children's program.