Depending on location, it could be very radioactive... I studied and worked at lab that did measurements, and it was push for closing a nuclear plant in our city (in Siberia) for coal-based plant, but after evaluation of waste, it was decided to continue to use nuclear-based station.

The problem with coal waste is that most of it is in the atmosphere causing climate change. That might not seem like a storage problem but it is. You can't put the genie back in the bottle.

To me, it's like someone asking where me to choose which part of my house to infect with wood rot:

1. A single scrap of wood, extremely badly affected, stored in a sealed box under the stairs

2. My entire roof mildly affected by rot.

I'd take the box under the stairs.

“Natural” as opposed to? :)