Two things come to mind for my area.
The signature dish for Delaware is
scrapple. It's more a regional dish, all across the Delaware Valley, but most scrapple is made in Delaware, so I think we get to claim it first.
The signature dish for Wilmington is "
Thanksgiving dinner on a roll". Here, it's called a Bobbie, since that's what they call it at
Capriotti's, where it was invented. On that note, this is kind of a specific restaurant/establishment, but is in transition. I think I can include this as Wilmington's signature dish because in the past few years, it's swept the nation, partly due to Capriotti's expansion in 10-12 states.