YARN is a four-year-old literary journal that publishes original short fiction, poetry, and essays for young adult readers. It’s a nonpaying market open to teens and adults, and they run at least one contest a year with gift card prizes. For example, they just held a Fall Treats Contest.
If you need a writing prompt to get you started, Kerri has one about everyone's favorite day of the week:
WRITING PROMPT: Rebecca Black, Katy Perry, The Cure—they’ve all sung songs about Friday. And we love to sing along. Now it’s your turn to pay homage to this special day of the week. Write an essay about something that really happened to you on a Friday, or make up a story about an outrageous Friday, or pen your own poem-song about the day. Whatever you do, make sure that Friday as a day of the week, a theme, or even an epic, permeates your piece from start to finish.