Among all of the suggestions from other writers who are in much the same boat as I, one of the most interesting and easy to use resources I found was the Duotrope's Digest. It is a listing of hundreds of publishing options and there is something for everyone including poetry, short shorts, short fiction, non-fiction, novelettes, novellas and full length novels. By simply plugging in the type of writing you are trying to publish, the genre it falls in and some other specifics (like pay vs. no pay), Duotrope's Digest will create a list of print publishers that are looking for the type of writing you are seeking to submit.
I did some research and found a handful of magazines and literary magazines that I think will be a good fit, and started submitting. Many of the magazines / journals allow multiple submissions provided you let them know if another publication purchases printing rights. I'm a little tentative, so for now I'm just going to go through one at a time.... at least until I get impatient and want to speed the process up a bit!
Check Duotrope's Digest out today here.