This is where the heck it is!
This door is located in A) Gotham! That's right, New York City--not anywhere in Europe. Where exactly? On Belvedere Castle in Central Park. Built in 1869, this Gothic/Romanesque hodge-podge of a building is made of Manhattan schist, a type of mica you'll find in boulders all over Central Park. For years, the castle served as a weather station, first housing the New York Meteorological Observatory and later the United States Weather Bureau. Oh, and that bronze critter on the door is a cockatrice, not a dragon.