The Council of Literary Magazines and Presses estimates that there are 600 actively published today; Poets & Writers lists 1,109 in its database. How do you even begin to sort through them?
I don't have a definitive answer. But here are some of the readings from two classes I'm teaching in writing for literary magazines. Most of these are incredibly short; you can read them in under ten minutes. They come from a range of interesting publications. Check them out. Maybe you'll find the home for your next piece.
Over the next two days I'll post a sampling of nonfiction and teen fiction, too.
Fat Man and Little Boy, a novel excerpt from Gone Lawn
Blind Spot from Origins Journal