I wrote poetry before I started writing short stories. I posted a lot of my work online before I knew that posting it online meant that it was published, and I could therefore not sell anyone else first publication rights to it. I might collect those poems and self-publish them someday. For now, I am looking at online markets, some of which pay and some of which do not.
I have had poetry published (years ago!) in Mediphors Magazine and in Teatime in the Oleander Garden: A Collection of Writings by Southern Women. Unfortunately, both of these fine publications are out of print. I can't even find them on the Internet. They both liked the same poem.
A place where I have recently had a poem accepted is The Plum Tree Tavern, an online literary magazine run as the blog of Russell Streur. He likes poems dealing with nature, and he wants them to be specific, about things you as the poet have personally observed rather than speculated about or imagined. It is pretty much how Emily Dickinson wrote her poetry.
If you are just stepping into the world of poetry writing, you might give All Poetry a look. It is a place where you can post your poetry and get critiques on it. Be warned, though, if you publish it there, it is published, and you will only be able to sell it elsewhere as a reprint or in a collection that you self-publish. So keep your really important poems off the Internet or in a private blog until you are ready to submit them to markets or publish them yourself.