The phrase "the island of Manhattan" primarily employs metonymy as a type of figurative language. Metonymy involves using the name of one thing to substitute for something closely associated with it. In this case, "Manhattan" represents not only the physical island but also the broader cultural, social, and economic significance associated with that location.
You could also argue that it encompasses synecdoche, a specific type of metonymy where a part of something is used to refer to the whole (or vice versa). Here, "Manhattan" might be seen as representing New York City as a whole, given its prominence.
In a broader sense, the phrase can evoke imagery and context to create a vivid picture in the reader's mind, which is characteristic of figurative language as well.