While living in California, I didn't realize that state doesn't have Coney Islands. Growing up on the west side of Michigan, they weren't a big part of my growing up either, but now that I live on the east side, coneys are everywhere, sometimes even across the street from each other, and I would be sad to again live without them.
If you are scratching your head and don't feel like clicking the links, I'll break it down for you. Coney Island is the name for both the type of hot dog, also known as a coney, and the restaurant that serves them. More than likely this diner style restaurant is Greek, and coneys are usually on the menu alongside the also very tasty gyros (pronounced, more or less to the American tongue, "yeer-ohs," and yes, with the sibilant s attached). Traditionally, coneys are hot dogs in a bun with chili, chopped onions, and mustard on top. One common variation popular in Ohio is to also top this with cheese (sometimes called a Cincinnati coney dog), which is my favorite way of doing things.
When I was reading about coneys on Wikipedia, I came across something called the Michigan, which seems to be what people in New York call a coney dog because coneys originated in Michigan. (In Jackson, actually, about a twenty minute drive from my apartment in Ann Arbor.) I have never heard of a hot dog called the Michigan, but I am delighted that we have one named after us.
Coney dogs are easy to make at home. I made some the other day when I had a bunch of hot dogs (Meijer sells turkey dogs in packages of 8 for $1.50), but was kind of sick of hot dogs. I had a can of chicken chili from Trader Joe's - the best one they sell - in my cupboard and a bunch of shredded cheese in the fridge. I didn't have any onions to dice, but unless they are sweet onions, they bother my stomach anyway. All you do is cook the hot dog, put it on a bun, squeeze on a line or two of mustard, and spoon on the chili!
If you want onion to make it "traditional," this is when you also spoon on the diced onion, and if you love cheese like I do, you finish by covering the dog in shredded cheese, usually cheddar, but it's really up to you since this is your coney. I used a blend of cheeses. Don't wait for the cheese to melt or try to force it to melt. Just serve fresh and eat as is, a hot and delicious mess.
And there you have a traditional Midwestern style of hot dog. I apologize to the rest of the world for not having Coney Islands. It is truly their loss.