Some popular magazines that accept short story submissions are Esquire, The Atlantic and The New Yorker. However, according to the Writer's Digest, it is becoming increasingly rare for consumer magazines to publish short fiction and, for this reason, increasingly difficult for new writers to get published this way. Although it is still possible to submit short stories to such magazines, new writers have a better chance of publication by submitting to literary journals.
Literary journals are typically available at local libraries and can also be subscribed to individually. Many accept electronic submissions and offer payment for published stories while others send published writers free copies of the journal or no payment at all. Some literary journals that accept short story submissions include the Antioch Review, Apocrypha and Abstractions and the Apogee Journal. Some journals have a specialist theme, such as Apocrypha and Abstraction's focus on surrealist and darkly psychological tales, while others are more general in their scope. A full directory of literary journals can be viewed at the Poets & Writers website.
An alternative option for writers wishing to have their short stories published is to submit work to an anthology. While anthologies put together by large publishers tend to favor established writers, independent publishers may be worth approaching for those who haven't been published before.