Tin House is a literary magazine of some repute:
The first issue of Tin House magazine arrived in the spring of 1999, the singular lovechild of an eclectic literary journal and a beautiful glossy magazine. Publisher Win McCormack said of the effort, “I wanted to create a literary magazine for the many passionate readers who are not necessarily literary academics or publishing professionals.” With the help of New York editors Rob Spillman and Elissa Schappell, along with managing editor Holly MacArthur, McCormack accomplished just that. Tin House offers an artful and irreverent array of fiction, nonfiction, poetry, and interviews as well as columns on food and drink, out-of-print and underappreciated books, and a literary crossword puzzle. Perhaps most indicative of the magazine’s mission to stake out new territory and showcase not only established, prize-winning authors is its commitment that every issue include the work of an undiscovered fiction writer and poet.
They are open from September 1 to May 31 each year, but I can't find any payment information (kind of tends to be the way with even the fancier literary magazines). They accept poetry, fiction and non-fiction up to 10,000 words.
Listing here: https://literarium.net/market/tin-house/tin-house