I once suggested that we put it into orbit, probably around the Sun. That meant it was far enough away not be harmful, but close enough that when conditions were right, it could be recycled into usable resources.
Put into stable orbit around the Sun both gets it away from Earth and also available if in 800 years we find a good use for it to be recycled. If, on the other hand, there's never a recycling use found for it, it can safely decay for a few thousand years till it's harmless.
It's probably cheaper overall to put it into stable solar orbit than trying to dispose of it safely on Earth. And a stable orbit means that it's location can be accurately determined for thousands of years. Possibly even specifically locating "Nuclear power waste in this sector, medical nuclear waste in that sector, excess plutonium in that sector, ..." etc.
To day's deserts may be tomorrow's urban areas. Imagine how much it would cost to safely clean up a huge area that's been contaminated by nuclear waste.
Back when the world wanted kerosene for lamps, the 'rubbish' petrol/gasoline was discarded for many years. That petrol would be very valuable today, but it's been lost.
