As for the Topic of the Day...
I'm guessing my first hamburger was probably from McDonald's or Roy Rogers. Or it could have been cooked on the grill in the backyard of our house on Walter Reed Drive in Arlington, VA.
Like DR John G, I also like a fried egg on my burger from time to time, but usually with a slice of pickled beet on it too - it's a very Australian thing. Otherwise: bacon, bleu cheese, caramelized onions, sauteed mushrooms, bread & butter pickles, swiss cheese, etc., etc., etc....
I'm trying to think of my current favorite burger in New York City, but no particular burger/restaurant is coming to mind. However, I can't really think of a burger I really don't like in New York City.