Woah, get out a little more man! You could probably just hit up one place a week in the haymarket and never regret it.
Another one that nobody has mentioned is Buzzard Billy's, also in the haymarket. I know its not local per se, but I doubt they have it in Washington. Really good Cajun food and some of the best hush puppies I've ever had. Only better southern food I've had comes from my Mom and her family. And you can try alligator while you're in Nebraska if you eat there, tastes like chicken (no joke).