The Front Porch Journal is an online literary magazine published by Texas State University in San Marcos. They publish three or four times a year, with a mixture of fiction, non-fiction, poetry, book reviews, and interviews, including audio and video features from time to time. They’ve been publishing since 2006 and the current issue online (as of this writing) is Number 18.
You can also find Front Porch Journal on Facebook.
If Front Porch seems like the kind of place you’d like to submit, you can do so online. They accept fiction up to 5500 words.