There are so many terrific authors of short stories to choose from. Jack London wrote several engaging short stories about early pioneer life in Alaska and animals, also Mark Twain's The Celebrated Jumping Frog of Calveras County is the humorist at his best, Washington Irving or Edgar Allan Poe have all penned wonderful short works if you need an American author for your project. If you wish to read a story by an author not born in the U.S. Rudyard Kipling, Arthur Conan Doyle, Aldous Huxley or James Joyce"s Dubliners are all stories that are well written and will offer cultural insights that are acceptable class material.
Without more information to go on, let me suggest two authors: Anton Chekov and William Saroyan. Chekhov's short stories are classic blends of style and philosophical content -- each a gem of description and characterization, revealing both the mise-en-scene (the world of the plot) and the psychological/spiritual state of the main character. Saroyan's stories, set in the California cities and towns of his life, are poetic descriptions of poignant moments that reveal the deep-seated affection for humanity that Saroyan carried with him, even into his more famous plays such as Time of Your Life and The Cave Dwellers. Find a collection of either author, browse, and choose something that catches your eye.