At what town or city does this story take place?
This is kind of a trick question. Truthfully, the "town or city" the drama takes place is really unimportant. In fact, the "town or city" is never even mentioned. It is not significant. That being said, I can be more specific about the setting for you.
In the words of Mark Medoff, Children of a Lesser God is set in "the mind of James Leeds." It is about James' memory and James' experience. However, there are two different "sets" per se. One is the State School for the Deaf (even though the actual state is not important). The second is simply James's house. Further, in regards to stage direction, there is a very purposeful minimalist perspective with very few props and very few set pieces. There should be no doubt that the author wants us, as readers and watchers, to focus more on content! Specifically, Madoff wants us to concentrate on the identity of Sarah:
These boys really liked Sarah, treated her the same way they treated Ruth, with respect, and ... and if you didn't know there was a problem, you'd have thought she was perfectly normal.
Although it is certain that the movie Children of a Lesser God has to have sets from a certain "town or city," that does not mean the original written work placed importance upon that physical setting. This is true of Medoff's original goal: to write a work of literature focusing on the issues of communication (and not necessarily of the deaf) and the struggle for identity.