If you are unpublished. Looking into different magazines that try to help new writers become noticed is Glimmer Train Press and The New Yorker magazine. I have a subscription to The New Yorker magazine and the stories published are slick. Meaning they are contemporary writings. There are realism stories along with the contemporary. Throughout the magazine you can read about the major events happening around NYC. It covers theater productions, musical productions and art exhibits.
I have submitted a couple of short stories to Glimmer Train Press. They have many contests throughout the year for unpublished writers to enter. There are several categories to choose from, and different deadlines. For example the short-short story contest deadline is April 30. Their website http://www.glimmertrain.com/ provides information on costs for entering and the guidelines for your writing submission.
Besides these two magazines there are many more writing contests to be found just using Google. So good luck!
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Writing Tips for Beginners 