Storage of long lived nuclear waste is often considered a major problem. There are suggestions of firing them to the sun (worst idea ever), burring them in subduction zones (a bit more sensible) or in special sites with plenty of warning for future generations (artists get creative on this one).
The thing is, nuclear waste may actually be among the most valuable things on earth. These elements do not exist in nature, and producing them require nuclear reactors and enriched uranium, which is a finite resource.
Even today we have the technology to burn nuclear waste in fast breeder reactors, though for some reason we haven't made a lot of progress, maybe it is not commercially viable compared to more conventional reactors. This has the potential to supply us with energy for so long that we can effectively consider it renewable energy.
All that to say that in the future, nuclear "waste" may become extremely valuable. I find one particularly ironic quote from a suggested warning message for long term nuclear waste storage sites. "This place is not a place of honor... no highly esteemed deed is commemorated here... nothing valued is here." I find it extremely dismissive of future humanity, as if we somehow reach the peak of technological progress and that future generations will be cavemen.
The risk that reprocessing can produce weapons-grade plutonium has been one reason. [1] Frustrating not only because it makes it unavailable as an energy source, but, as I understand it, the waste products from fast breeder reactors generally have much shorter half-lives than the current waste.
The decision not to do reprocessing was based on 1970s cost/benefit analysis. We're in a different world now.
Dull thuds in the distance as dark masses streak across the sky every 10 minutes.
Futurama Season 1 Episode 8, "A Big Piece of Garbage": https://en.m.wikipedia.org/wiki/A_Big_Piece_of_Garbage
Edit: in Utah
Amusing. Why not a section of marsh? Or river delta?
#LizardLivesMatter
Always struck me as interesting in that you could easily section off a chunk of desert, properly sort and encapsulate the trash. At the same time fund research into ways to do recycling that is more cost efficient and more environmental friendly with regard to chemicals used, etc. Then once you have better tech for a certain class of garbage, go process it in bulk.
Of course humans being humans, we'd probably not bother to fund the research, not do upkeep on the encapsulation material and mess up the ground water, etc. Still interesting to think about just having one or two national trash dumps.