Just thinking aloud here...

This was one of the more generic ideas I got from reading science fiction--not that the idea is generic, but rather the thought of it. It's a given, in other words. When reading sci-fi I think of today, only more so (as the famous saying goes). We have local libraries now, so why not a global library?

But what works so well for civ archives in sci-fi is that the authors think every civilization worthy enough will have an archive. I think this is because a sufficiently advanced species will have unified its societies into a global one, and therefore be able to archive the achievements of each society in an agreed-upon manner that will allow any of the individual societies to access the archive without others around.

In order to ensure the survival of such a thing, I agree that the moon would be a great place for it. To access them, we could use satellites. This reduces the chances of losing access to it since satellites are, obviously, unaffected by terrestrial catastrophe. We just need to make sure there's always computers left to gain access to the satellites, which really isn't too much of a problem considering how small and rugged we can make sat uplinks.

Good stuff. Thanks for the thought, Jamais.