New York Hot Dogs
Brooklyn Matzoh Balls
Brooklyn Cheesecakes (Junior's Restaurant reference - look it up)
Philadelphia Cheese Steaks
Boston Baked Beans
Boston Clam Chowders
Vermont Maple Syrups
New Jersey Peppers and Eggs
Pennsylvania Pretzels
Kentucky Fried Chickens
Kentucky Pulled Porks
Texas Barbecues
Kansas City Barbecues (imagine the Texas-KC rivalry over name use: it would like the controversy between Greece and Macedonia over the use of the latter country's name).
San Francisco Rice-a-Ronis
Cincinnati Chilis
Iowa Beefs
Chicago Deep-Dishes

What other ones can we think up?

'course you could also do a whole Italian regional food name based Baseball League:

Vicenza Baccalàs
Napoli Pizzas
Bologna Mortadellas
Bologna Ragus
Sicily Canolis
Cremona Pumpkin Raviolis

and so on...

Mississippi Mud Pies

Florida Fried Twinkies

Having grown up in Boston--

Boston Steak Bombs (a steak bomb is a form of cheese steak that has peppers, onions, mushrooms, and sandwich pepperoni)
Boston Lobster Rolls (every bit as good as they are in Maine, maybe even better)

I once had a team in a league called the Baltimore Charm City Cakes (shout-out to Duff Goldman, who used to wear a Norwich hockey jersey, because the owners of the production company were fellow alums)
Baltimore Crab Cakes

Living now in southern Arizona--

Arizona Chimichangas (claimed to have been invented in Tucson)
Arizona Sonora Dogs (Hot dog wrapped in bacon, covered in beans, cheese, jalapeno, and condiments...mmmmm, Sonora Dogs!!!!!)

Utah Fry Sauces. Fry sauce is a concoction used as a dip or topping for French fries,and, would have been the “go to” companion for French fries as opposed up ketchup. I believe it’s a mixture of ketchup and mayo. Very common in Utah and maybe only in Utah.

Toronto Veal Sandwiches

Pittsburgh Pierogies
alternatively: Pittsburgh Primantis

Brooklyn Bagels
Manhattan Clam Chowder (better if it's singular ;) )
Brooklyn Coneys
Coney Island Franks / Coney Island Dogs

Atlanta Grits

Jersey Pork Rolls

NY Cronuts

Pennsylvania Knishes

St. Louis Toasted Raviolis

California Avocados

Tex-Mex is the best food on Earth. Could make a whole league outta that. Along with all the BBQ stuff of course

Texas Chili Con Carne
Houston Fajitas
Texas Enchiladas
Houston Queso
Texas Porterhouse
Houston Brisket