This is already in one of your answers, but Luna is, in my opinion, an excellent candidate for several reasons:
1) The placement and size of the moon is perfect for keeping the earth's axis from wobbling. This prevents, for example, half the planet from entering permanent day or night when the axis wobbles to face the sun. This has happened to Mars in the past and is theorized to be one of many reasons the red planet doesn't have large amounts of life.
2) It's large enough to house any number of highly technological constructs without risking their detection.
3) The capabilities of a Type II civilization are so far beyond what we are currently capable of that we don't even know if such a civilization would need to have actual monitoring equipment as we know it. For example, they may have forged a deep connection with the universe in order to "borrow" data storage and processing power from the universe itself, such that their thoughts don't necessarily have to happen within the confines of their own brains. This would render them effectively omniscient, so monitoring equipment would be beyond redundant. If this were the case, the only evidence of their interference with the earth might just be in the odd coincidences that resulted in life on Earth.
4) The moon represents an interesting candidate because one side always faces the earth, so any technological constructs could easily be hidden on the "dark" side of the moon under a small layer of dust without damaging broadcasting capabilities, and it could also serve as a plot device allowing governments to keep the discovery of such a facility a secret from the general public. Excellent fodder for the conspiracy theory crowd.
5) So much of our biology and culture is related to lunar cycles and changes that discovering that it is artificial or that it was placed there as some sort of extraterrestrial intervention would send shock waves throughout all human society. Gestational periods of human women, mathematical conventions for measuring angles and other geometric constructs, architecture both ancient and modern, and pretty much all life on earth reflects strongly the influence of our primary satellite.
If you dig into it, some happy accidents of mathematics occurred because of the influence of the moon on human culture. If an artificial satellite created or at least influenced in some way by a type II civilization is a central plot point for you, I believe the moon would be an excellent choice because of how powerful such a revelation would be to the whole of mankind.
18Surely the advanced aliens have microelectronics and whatever they use to monitor us is tiny. A few devices on the moon that take pictures of earth, monitor radio signals and beam the data back using lasers. The devices could be small and well disguised. see cubesat – Donald Hobson – 2017-03-18T15:12:35.517
29This is a GREAT question. I nominate it for Question of the Year. Specific, on topic, short, interesting, drawing on science for a hypothetical result. THIS is a great WB question in my opinion. – SRM – 2017-03-18T16:10:24.717
@SRM I completely agree. You;ve got my vote. – Tonny – 2017-03-18T16:18:01.937
Maybe Moon is artifical object? - http://www.theforbiddenknowledge.com/hardtruth/moon_spaceship.htm
– vodolaz095 – 2017-03-18T18:42:03.307A bit far, but maybe Mimas?
– Darkest of Nights – 2017-03-18T19:55:32.6272What about the sun? I'd say it would need to be in the last place we could ever explore. – n00dles – 2017-03-19T15:24:17.147
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– n00dles – 2017-03-19T15:34:00.71715"No ... ninth planets allowed" Poor, poor Pluto. How quickly they forget. – Steve-O – 2017-03-20T20:43:54.033
4"All these worlds are yours - except Europa. Attempt no landings there." – Grimm The Opiner – 2017-03-21T09:42:51.340
I suggest Rupert. – Whelkaholism – 2017-03-21T10:24:58.737
1IMO, most interesting would be Neptune's odd moon, Triton. Too far to be examined closely by us, too big to be likely considered artificial, but odd enough that artificiality might explain it, e.g., its retrograde orbit. Potentially in reach of a Type II civilization (though we have no good idea what's possible). Also, potentially dramatic enough to indicate what level of civilization might accomplish it. – user2338816 – 2017-03-21T10:59:41.903
https://en.wikipedia.org/wiki/Mutineers%27_Moon I really like this one. In order to hide the ship, they hollowed the moon. Then it got left there for ~20,000 years – Roger Willcocks – 2017-03-22T02:59:31.503
I'd just like to point out that you linked us to the mobile page :) I can't edit because I can't find anything else which is wrong with it (great job there), so could you? – Restioson – 2017-03-22T16:10:42.973
What about Halley's Comet? It comes around once every ~80 years which is frequent enough to check for a major change in technology, but between visits stays too far away for us to investigate it too thoroughly. Additionally, it is such a recognizable name that you won't have to worry about readers not being familiar with it. – Brendon Dugan – 2017-03-22T22:08:03.147
Not one shout for Ceres? The biggest object in the Asteroid Belt and, I'd say, just on the edge of people's minds being, once upon a time, an interesting object (but nowadays relegated in interest). – Zorawar – 2017-03-23T00:38:31.663
Is there a reason that link is to the moible form of wikipedia and not the full version? – Pharap – 2017-03-23T03:14:21.523
@Steve-O I support you, fellow planets-must-never-be-reclassified-as-non-planets believer: this is why I still consider Ceres and several other bodies in the asteroid belt planets. – mtraceur – 2017-03-23T09:19:49.753
@Restioson sorry, wrote this on a phone and it just kept autocorrecting to the mobile link. Should be fixed now – Timpanus – 2017-03-23T10:30:35.827