From what I can read there are many contradicting informations. At least with scientists here. Some say the "area" is save. others say it might become instable in the future. Who knows.
This really ain't complex science. You have three types of radiation emitted from nuclear material/waste - alpha, beta, gamma. Alpha is potentially by far the most dangerous but, as with beta, can be *fully* contained by any number of basic materials - iron, wood, lead, concrete whatever, even for beta containment it need only be a couple of inches of almost anything. Alpha is a particle, beta a subject of duality, gamma a wavelength of the E.M. spectrum, hence it's harder to contain (but the least dangerous by far). You can never entirely contain gamma rays, however a pretty cheap reinforced concrete container can do so to the extent that exterior radiation levels around it will be virtually background. The problem is longevity, as such a container (if it's on the cheap side) can only be guaranteed for 30 odd years.
Still, containment that will be secure for 100+ years isn't expensive, for small amounts of material anyhow. The ideal solution would be a large underground facility that would provide containment for 100+ years and cater for very large quantities of waste. Admittedly such a facility would cost a bob or two.
I agree that energy source diversity is required and that technological developments concerning fossil fuel combustion are promising. This doesn't detract from my point, that being many Western nations could benefit environmentally and financially from a greater level of nuclear fission (and waste disposal facilities) reliance than we currently see.