Launch it on a rocket. Send it to the sun. Once it leaves earth’s gravitational pull. the sun’s gravity will take care of propulsion for the remaining trip.
Rocket better be foolproof, you don’t want a rocket full of nuclear waste going boom a mile or two up. Musk has made it cost effective though. But more importantly, we now know how to use it until it’s in a state where it only needs to be stored 300 years instead of 100,000 years.
The problem with wind and solar is that they will ALWAYS have their limitations - no wind no sun no power! At some point if/when fossil fuels are either outlawed or exhausted there will be a need for source of power that can be relied on 24/7.
And if the millimeter laser drilling pans out the entire problem is solved, geothermal for the win.
Which is why I have always said, fifty years from now this debate is going to look like arguing about where we were going to put all the transport related horse manure as cities grew.
The most likely scenario if we did that would be for the rocket to be slingshotted around the sun and ejected on the other side, possibly right towards Earth. It would take far more rocket fuel to overcome this phenomenon, and though I don’t know the exact figures, it becomes cost prohibitive and impractical in general. The slightest glitch and it goes careening off in who knows what direction.
Again, new advanced reactors can use that waste as fuel and the end product becomes safe after 300 years vs 100,000. And the problem with sending it to space is the danger of the rocket failing in atmosphere. And to get it out of earth orbit would be very expensive, no need to shoot into the sun, space is kind of big.