New York, New York—so nice they named it twice. Bishop doesn't come out and say that this poem is about The Big Apple, but based on her own biography (check out "In a Nutshell"), it's a good bet that this is where the Man-Moth prowls.
Setting the poem in the city gives Bishop a whole lot of contrasts to work with. A moth is a tiny and natural creature, while the buildings in New York are so big and manmade. Moths are fragile with delicate wings, while the buildings are cracked and battered. We just get the overall impression that the Man-Moth isn't in his element here, and it creates a level of tension that wouldn't be the same if he were on his front porch in a rocking chair chewing on a piece of wheat before he tried to fly up to the moon. Context is everything. The city also makes it a lot easier for us to accept that something strange like a man-moth is worth investigating instead of running away from. Weirdness like that is almost expected in a place like New York.
The tension wasn't just limited to the poem, either. Bishop had just moved to the city for the first time when she wrote "The Man-Moth," and it was an overwhelming experience. Not only did she feel out of place, but her health was also often a problem each time she lived in the city. Bishop became depressed and turned to alcohol to soothe her anxieties. It is a bit of personal irony for her since it was The New Yorker that gave Bishop her big break in the literary scene, but the city also made her physically and psychologically ill. "The Man-Moth" isn't the first, nor would it be the last, of Bishop's poems that are either about or set in the city that never sleeps.