One I came up with today is a rather simple one that could probably be put anywhere. Given it's in an urban area, there are probably people that are actually supposed to go through this door. Give each one of these people a small snake-shaped object, including an open mouth. The door can simply have a hint of "Infinitely open" either inscribed on it, or discovered through some other way.
Now, there is no access to the lock on the outside, so it can't be picked, but that snake object is necessary to open it. Inserting the tail into the mouth will create an oroboros loop, which then opens the door when touched.