EMILY: And what do you intend to do with that paper clip?
LORELAI: I intend to carve something really dirty into the bathroom door … What rhymes with Nantucket?
Nantucket, an island about 30 miles from Cape Cod in Massachusetts; the main town on the island is also called Nantucket. European settlement on the island began in the 17th century, and it was a major centre for the whaling industry by the 19th century – it features in Herman Melville’s novel, Moby Dick. Since the 1950s, it has been an upmarket summer colony and popular tourist destination.
The island features in a famous limerick which begins, “There once was a man from Nantucket …”. The original, written in 1902, is:
There once was a man from Nantucket
Who kept all his cash in a bucket.
But his daughter, named Nan,
Ran away with a man
And as for the bucket, Nantucket (“Nan took it”).
It spawned numerous sequels, many of them vulgar in nature, because the island’s name rhymes with “fuck it” and “suck it”. The earliest such example was published in 1927. It is a staple of American humour, with the name itself enough for listeners to understand the allusion, as in this scene.
The Annotated Gilmore Girls 