Things that are in plain view but are passively overlooked:
graffiti, paving structures, chimneys, numbers on lampposts.
Things that are in plain view but are actively ignored:
litter, garbage tins, dog shit, beggars and homeless people.
Things that are out of view:
underground cables, pipes, drains, alleys, back-sides of buildings.
Phenomena that are out of view:
ground water levels, geologic strata, the Mohorovicic discontinuity.
Things that have disappeared into history - but are still present in memory - more or less:
ice age soil structures, settlement history, vanished buildings, the snow of yesteryear (Jacques Villon).
Phenomena too faint for the human senses:
gravity variations, magnetic deviations.
Phenomena that are outside the scope of the human senses
infra-red light, ultraviolet, infrasound, supersonics, radio waves.
Things that happen while you are elsewhere:
wild animals that roam the city streets unnoticed while you sleep, the car crash that happened just around the corner.
Things that exist but are too big or abstract to see:
the power- and economic structures that determine how a city grows, the global economy. (Like the names on maps that are too big to notice. (E.A. Poe)).
Things that are kept hidden on purpose:
crime, espionage, corruption, fraud.
Things that exist only in fiction - but can be imagined at a specific spot:
site an itinerary descriptions in literature (Malte Laurids Brigge), mentions of real places in fictional accounts (Rotterdam is mentioned in V by Pynchon and the Demon Princes series by Jack Vance).
the site of the first kiss, the sites that remember what I played on my mp3-player when I was there once.
ghosts, EVP, the "stone tape" hypothesis.
Each of these modes of invisibility can be used to experience the city in a new inspiring way. Each one should be tried - at least once.
I am fully aware that his is not a proper taxonomy. But it is workable starting point. Feel free to add your own items.