Stored indefinitely until a curious explorer decides to investigate the unknown tomb of the gods of the third millennium, and… voila. I’m convinces we’ll solve storage by reusing the waste - but it’s not a solved problem by any stretch.
Voila what? If you're concerned about people degrading so far down that whatever we leave behind is "tombs of the third millenium", then storing a truckload of nuclear waste isn't really an issue.