I don't know that Reno has a local dish exactly, nor is there really anything that this little corner of Nevada has contributed to the world itself.
But since this is a town of transients, there are a lot of great things brought in from elsewhere---dynamite Mexican restaurants, a pizza place run by Displaced New Yorkers that wouldn't be out of place on 42nd Street, a Philly cheesesteak place run by people from Philadelphia, enough sushi joints run by Japanese people to keep an anime convention in hand rolls for days, and all the California cuisine your little heart can handle (which in my case is "none" since I hate the stuff, but some folks like it.)
Only real problem as I see it is the severe lack of good places to get a cheeseburger. You're pretty much limited to Carl's Jr. if you want a decent slab o' ground beef. I dearly miss the roast-beef-shop cheeseburgers that can be found just about everywhere in my New England hometown. Looking forward to moving back next year.