The Doomsday Vault on Svalbard.
It's tempting to say that we wouldn't need such a long period to reinvent culture today. The world is more interconnected, so nothing short of a global catastrophe could bring about the same effect, and there is just more information available in more places. Tempting though these arguments are, it would be nice to have some further insurance that four centuries from now, an illiterate farmer plowing a field on top of what they don't know is the ruins of London will stumble upon a durable and intuitively understandable recording of basic knowledge. After all, it would save your descendants some sweat and tears.
What would we tell them? It should essentially be a naked-eye-readable Ikea-like manual for how to re-invent civilization, with a basic primer in how to sound out the Roman alphabet of course. We shouldn't so much care if they have a list of our kings as whether we can tell them the basics of agriculture, law, physics and biomedicine.
Such a plan raises the question: who cares? Are we doing this to spread our memes for their own sake? Did the British care after the loss of their middle American colonies that despite the loss of immediate revenues to the crown they had just sown the seeds to future hegemony of Anglophone values? Would the Hittites have cared that they could save the Romans or Persians a misstep or two by making sure their own military and political expertise were handed down through the ages? Such a project could only be undertaken out of compassion for people in possible future Dark Ages. In the short run the American Revolution certainly wasn't a benefit to the British Empire, and as Keynes said, in the long run, we are all dead. Indeed it's hard to think about morality in these terms, discussing people that don't yet and may never exist, whether or not they're related to you.