The back of the moon, Mars, the asteroid belt, or various moons throughout our solar system would make a much better base, in my opinion, than the Earth. Why? Because it's easier to hide them off of the Earth. There could even be ancient, abandoned ET bases or colonies throughout our solar system. I think SETI should be looking for archaeological evidence throughout our own solar system instead of listening for radio signals.
If there are alien bases here on the Earth, you can bet your ass that probably no one knows where they are, not even the top-military brass. (see Dulce, NM, myth).
If there are alien bases here on the Earth, my guess is that the aliens actually live here, on the Earth, and communicate with their homeworld in a way that is fast and undetectable. We may be subjects of a galactic empire without even knowing it. The advantage of this is that we would have protection from hostile alien invaders, comets, asteroids, etc.
Of course, all of that is complete speculation. I don't pretend that I have any data to back any of it up. But this question is fun to think about.
Imagine what that Star Trek episode would look like. Captain Picard and the Enterprise come upon an uncharted system with one inhabited M class planet, a pre-warp civilization. But, what's this: sub-space communication signals coming from deep below the surface? Are the poor little darlings living on this planet being controlled and constantly decieved by a group of super-advanced aliens living in underwater and underground bases? Oh, my. Mr. Riker, what should we do? Should we abandon the prime directive and liberate these poor saps from those goddamned bastards who have imposed various religions and ideologies on them and who continue to abuse them in bizarre abductions throughout their lives? What kind of madness is this, Mr. Riker?
