"Drop it into the Sun" people are always saying. Right. You would have to completely cancel the Earth's orbital velocity, some 66,000 miles per hour, to be able to 'drop something into the Sun.'
Nuclear waste must be managed actively until we can figure out how to dispose of it permanently. A fusion torch would probably do the trick, being hot enough to break down the atomic structure of matter. Just burying the stuff in the ground somewhere and forgetting about it would be criminal, because it will still be dangerous thousands of years later.
I object to building more nuclear power plants when the issue of waste has not been resolved.
Eventually, launch costs will be low enough, and reliability high enough, that we could get it off Earth. But we probably would be better off keeping it here, where we can keep an eye on it. Isolating it from the environment is an on-going process, because it will gradually destroy the container. (High level waste, that is. Low level waste can be buried above the water table, as long as it is in a non-porous form.)