As a Rochesterian, I can chime in on the "Plates" theme and the Garbage Plate. I'm not sure where it came from that plates have beans... they hardly ever do. They're almost always a base of homefries (similar to french fries), and a creamy macaroni salad, topped with two cheeseburger patties and meat-based hot sauce. There are sometimes substitutions - e.g. you can generally get them with hot dogs instead of hamburger patties, etc., but the "traditional" (and most common) plate is the homefries, mac salad, cheeseburger patties and hot sauce.
The meat-based hot sauce is unique to Rochester. It has a complex flavor and is spicy, meaty, and often has other ingredients like nutmeg and/or cinnamon. The "traditional" way to top a plate is with yellow mustard and fresh chopped onions.
The original garbage plate was created at local restaurant Nick Tahou's, and celebrated its 100th anniversary last year (hence the Red Wings adopting the temporary moniker of "Plates" in recognition of this anniversary). Many restaurants serve their own variations on the theme - "Trash Plate", "Rubbish Plate", etc., but over the years the menu item has been more or less genericized to "Plate." If you say to a fellow Rochesterian "Let's go get a plate", you know what each other are talking about.
Similarly, in Buffalo (or in Rochester), Wings are simply called "Wings". No one says "Let's go out for Buffalo Wings" or for "Chicken Wings" - that would be considered redundant.