I live in a burb of Indy. The best thing we have going is fresh produce. In the summer the farmers markets are awesome. Sweet corn and tomatoes specifically, but also strawberries, watermelon, squash, zuchinni, etc.
Indy itself is definitley not a culinary capital. Most people go to steak houses. St. Elmos, Moes, and Mortons are a few that come to mind. They each have a dish that they are know for.
Milk has always been the traditional beverage of the Indy 500 winner.
There is also alot of pork production in the region.
Maybe a mixed bag of sweet corn(on the cob), fried squash, zuchinni bread, anything made with red gold tomatoes, and either pork or steak.