Three times a year theThe Jerry Jazz Musician hosts a short story contest. There is no entry fee. Shorts should be 1000 to 5000 words. Here's what they're looking for "The Jerry Jazz Musician reader has interests in music, social history, literature, politics, art, film and theatre, particularly that of the counter-culture of mid-twentieth century America. Your writing should appeal to a reader with these characteristics."
The winning writer receives $100 and publication in their newsletter. You can find the details here