Yucca mountain was cancelled for political reasons--not because the site was insecure or incapable of storing the material. Basically Congress paid to build and complete the site but then didn't authorize the actual storage of waste there--all political games. Furthermore, the "waste" fuel can be reprocessed in breeder reactors to be used again instead of burying forever. The nuclear products remaining have much shorter half lives too, so long-term storage is not as much of a concern. France does this.
Finally, the amount of waste generated is absolutely minuscule. It's something like the size of a football pitch by 30m high for the entire history of human nuclear energy. That is incredibly tiny compared to the damage done in resource extraction for coal, oil, gas (or even solar and wind).
Even all the nuclear disasters combined have killed far, far fewer people than the widespread use of other energy sources, but people are afraid of big, scary events rather than common, invisible risks--the same reason people are irrationally afraid of shark attacks and airplanes instead of riding in a car of cheeseburgers and soda. Modern reactor designs have safety features that make them passively safe and virtually immune to meltdowns.
We could have had plentiful, green energy 30 years ago. Instead today we have fracking and natural gas because the anti-science hippy faction of the environmentalist lobby and ignorant NIMBYs (fueled by oil money and FUD) killed nuclear.
All the technical problems of nuclear are solved. Long-term storage isn't even a technical problem--it's a political problem where there is a major faction opposing it. It's sad too because we could have cheap, clean, and environmentally-friendly energy if or politics weren't so phuked.