Tin House is one of the nation's very best literary magazines, regularly placing stories in national anthologies and always full of impressive contributors. Tin House features literary work but has a flair for the entertaining as well, and includes some genre or genre-adjacent work as open. In a given issue you may find work by Stephen King or Ursula Le Guin. Tin House has offices in both Portland, and Brooklyn, and runs the Tin House Writers' Workshops every summer and winter in Oregon.
Started by Francis Ford Coppola in 1997, this San Francisco-based literary magazine features only fiction, and regularly publishes heavyweights of the literary world. Guest designers are behind individual issues, giving each issue a distinct look. Each issue also features a reprint of a classic short story that inspired a short film.
Perhaps the most San Francisco of San Francisco literary magazines, ZYZZYVA has always had a particular love and passion for West Coast writers. ZYZZYVA has been coming on especially strong in the last handful of years since Laura Cogan took over as editor and Oscar Villalon as managing editors, getting a number of stories and notables in the Best American Short Stories anthologies.
Fresno State's literary magazine, The Normal School, has established itself as a national name since it was founded in 2008. It's built a reputation especially as one of the premier outlets for interesting nonfiction, though it publishes great work in all genres. The Normal School is also a magazine with a distinct voice and personality, a great champion of funny and oddball writing.
This Berkeley-based literary magazine has a long history and a strong reputation. It features fiction, poetry, and memoir, but also criticism and commentary on film, literature, and drama. They are also one of the better-paying literary magazines: $400 for a short story and $200 per poem.
The Santa Monica Review, an LA-based literary magazine, has been publishing since 1988, with a special focus (though not an exclusive focus, if I have it right?) on writers from "Southern California and the Pacific Rim." It currently accepts submissions in fiction and nonfiction, but not in poetry.
San Francisco State University's literary magazine Fourteen Hills bills itself as open to progressive and experimental work. They are also open to cross-genre work.