Suppose there's an island in the East Pacific, west of San Francisco and south of Alaska (see Google Maps; there's nothing but ocean there). This island needs to be at least 4x the size of Manhattan, preferably larger. It's home to a diverse and loosely-governed society that doesn't care to communicate with the outside world. It's not owned by or connected with any external government. It's self-sufficient (no substantial exports or imports). And its government has a strong interest in keeping the existence of the island secret. That is, perhaps select individuals outside of the island can know about it, but if it were to show up on satellite imagery, a Rand McNally map, Wikipedia, etc. that would cause irreparable damage. Any ships, more than the occasional lone adventurer blown off course, would also be unacceptably inconvenient to deal with.
This is a non-magical world, so a Hogwarts Hidey Spell won't work here. However, the island's access to technology is quite good; perhaps on par with present-day American military/government research. The population of the island includes a number of millionaires and scientists who have disavowed the outside world and aren't interested in going back.
Assuming that the island's government has access to impressive wealth and a few privileged connections (as few as possible, of course), how could it keep the rest of the world in the dark?
EDIT: This question has been tagged as a possible duplicate. There are some similarities, but the accepted answer to that one was "hide in plain sight, under the guise of a resort/theme park". That's great for hiding an evil lair, but not nearly as good for hiding a civilization that loves its privacy.