That "waste" is fuel in a breeder reactor (or other advanced reactor designs). Current (ancient) reactor designs only recover a very small amount of the usable energy (something like ~3% of the U235, if I remember correctly?). Worrying about disposing of "spent" fuel out of fear for of it's current physical properties (radiation) is like worrying where we should store the "waste" 97% of the gasoline remaining in your car because you only allow an engine design capable of using 3%.
Waste has never[1] been a technical problem. The people creating the problem of waste are the people that push irrational fears about any new reactor designs that would solve the problem.
[1] a small fraction will always remain as waste, but that is something we have some control over by choosing the nuclear decay chain=, and it would still be a few percent of current reactor output. Even with current designs, the massive gain in energy density makes the current amount of waste trivial compared to the fly ash waste of coal power. Coal is worse even if you only consider radiation, and coal waste also contains heavy metals and other chemical waste that doesn't got away even with a long half life.
But where can you find such a place? In Germany people believed to found such a place in an old salt mine, now they have to get the stuff back before the mine is completely flooded with water and will contaminate the area around it. And that wasn't high radioactive waste. You need to store is from 100,000 to a million years and you need to inform people about it. Which isn't easy b/c we couldn't really understand the writings on the Pyramids in Egypt which were build just a few thousand years ago. Nuclear power is also dangerous because you can't easily tell apart if a country use it to generate power or build a bomb.
> In Germany people believed to found such a place in an old salt mine, now they have to get the stuff back before the mine is completely flooded with water and will contaminate the area around it
We're talking about the Asse II mine?
Yes, back in the 60s and 70s a research project was run to see if a salt mine would be a good place to store waste. In turns out it really, really, isn't because (spoilers!) salt mines aren't stable. Which is something we now know (and honestly could probably have figured out back then) which is why nobody is proposing on storing waste in salt mines any more.
And it's not completely flooded, and it isn't contaminating the area around it. It's in danger of collapsing, and now the waste needs to be moved somewhere else, yes., but it's not like it's hard to find stable locations; the issue with Asse II is they picked one that isn't stable.
> You need to store is from 100,000 to a million years
Waste that needs to be stored for "100,000 to a million years" is not particularly dangerous by definition. Either it's highly radioactive or it has a long half-life. It can't be both.
As for the hypothetical "future civilisation" which has somehow lost all our rudimentary knowledge of the physical sciences, but is still somehow capable of deep mining operations is a stupid, absurd canard. Any scenario whereby the knowledge about geiger counters is forgotten is one where that society's problems are going to be far, far more serious than a few deeply buried barrels of lightly irradiated surgical equipment that are statistically impossible to discover by accident.
Oh, and you do realise the stuff came out of the ground in the first place? Where's your concern for these future civilisations digging around in natural uranium deposits?
Great in principle, but sending nuclear waste hurtling through the upper atmosphere strapped to a tank of rocket fuel seems like a really bad idea in practice. You'd be one mishap away from spreading radioactive dust over a huge area.
Some kind of railgun-like launch system big enough to achieve escape velocity could work, I guess - but that technology's not there yet.
