Back in the 70s they used the Big Apple in the marketing for tourism in the city and it has stuck ever since. The mother likes Christmas decorations and I got her one of a big apple with all kinds of Christmassy crap on it. I mention this because I know you love Christmas.
A google search reveals the real origin but I prefer the fake one: The term derived from a New York brothel whose madam was known as Eve.
Let the imagination run wild!
In general Clive most places have quarter pounders I rarely see one smaller than that. The nicest one I had was in Williamsburg in Brooklyn (where a lot of hipsters live) but I cannot for the life of me remember the place. It was nothing fancy either just perfectly cooked with the right toppings.