You can start by searching online. There are many literary websites that list magazines along with their submission guidelines. For example, Duotrope is a great resource. It has a comprehensive database of magazines and details about what they accept.
Another option is McSweeney's. It's known for its eclectic mix of literary works. They are receptive to long short stories that are creative, unique, and well - written. They might accept a long short story that plays with narrative structure or uses an unusual voice to tell a story.
One benefit is wider exposure. Since these magazines have a readership interested in long stories, your work can reach a targeted audience. For example, if your story gets published in The New Yorker, it can be read by a large number of literary enthusiasts around the world.
The New Yorker is well - known for accepting long stories. It has a reputation for featuring high - quality, in - depth literary works. Another one is Harper's Magazine, which has a long history of publishing great long - form fiction. And Granta also accepts long stories, often presenting works from emerging and established writers alike.
Check with your local library. Librarians are a great resource. They can guide you to literary magazines available in the library's collection. Some of these magazines may accept short - story submissions. Also, they may be able to point you to directories or reference books that list magazines that are open to short - story submissions.
Another one is 'Outlook'. It often showcases short stories. It has a wide readership and is known for promoting diverse voices in literature. It gives a platform for both established and emerging writers to share their short stories with a large audience. It also covers different genres within short stories, be it mystery, romance or social commentary.
Most domestic magazines would accept short stories, but the specific magazines that would accept them might vary according to the region and subject matter. You can search for the name of the magazine on the search engine or consult the relevant publishing editor or editorial team to obtain more accurate information.