Start here:
poetrymagazine.org
They only accept original unpublished pieces. This is one of the last legit journals in the US. Check around for other contests such as the LA Times.
Shall I compare thee to a summer's day?
"That's right, Billy Boy! I'm hot and long!
Thou art more lovely and more temperate:
"Speak English, will ya' Will!"
And summer's lease hath all too short a date:
"I'm no short date, baby. I'm like that song, 'Hour Man.'
And often is his gold...