You're good enough for the nationals, no one disputes that; but after 5 or so years wondering why The New Yorker and Ploughshares don't publish you --
there's at least one literary journal or rag nearby. Your big city has several; your home state has a score. And, insofar as the fit is right, start submitting your work to those closest to home. Advantages:
1. Local editors will see your work and know you exist. If you're published, local writers will read your work (they're in the same journal) and when you meet them at literary gatherings (because you DO go) your name will sound familiar and you can make some friends.
2. Local writers will introduce you to local editors, because editors are writers too. See if you like them. Take them up on any offers to read their slush pile or hang out at headquarters. And then submit your best work. Do it soon-- before you're on their masthead.
3. Publish in two or three local journals and keep showing up for events, and local literati will seek you out for readings of your work.
4. Doing some readings may lead to teaching a workshop, judging a contest, or to a guest appearance in front of a college class. And somebody is always assembling an anthology. Now that he or she knows you, you might get asked to submit some work. Bingo; you go into a book without even trying.
I wrestled with the biggies and didn't get much of anywhere until I tried my homies. Does that mean I picked the low-hanging fruit? The above got me jobs that I live on, tons of great friends, and published. By their fruits ye shall know them!