There's a few projects like that already happening, like Github's code repository on Svalbard.
That said, I think one big reason why the artifacts mentioned - Sumerians, Mayans, Egyptians, or even Vesuvius - were preserved was because they were lost; buried in the desert, overgrown in dense jungles, buried under volcanic rock and ash, etc.
For something to stand the test of time, it has to be lost. Al-Quaeda and ISIS have destroyed visible historic monuments and documents, for example, and some people in the US are advocating for the removal and burning of certain books as well.
So yeah, underground caves and hidden monuments would probably be best, although the collapse of society may take care of that as well.
Another option: Time capsules of data sent out into space in
containers that can survive re-entry in thousands of years. Ideally with a lot of flashy light effects and a persistent smoke trail on re-entry.