Is the setting an important part of a story?

It really depends on the book and the author. Every book is going to be different. In cases like Ethan Frome or The Awakening, the setting plays an integral part in portraying the theme of the novelette. The themes of other books however, like The Scarlet Letter or To Kill a Mockingbird, don't really depend on the setting. You know the setting will play a vital role if it sets a tone that drastically affects the book or the character.