Even more than that, a nuke plant generates, amortized, several tons of waste per year. A few flasks. Which can get shoved into a volume the size of your garage. And then you basically forget about it. Unlike, say, a coal plant, which generates a reservoir worth of awful ash a year. Containment isn't even an option there.
Even more than that, even if our nuke plants vented directly into the atmosphere every now and then they'd still put out less radioactive waste than coal plants. Seriously, the only reason nuclear waste is dangerous is because it's concentrated. If we held nuclear plants to the same standards we do coal plants, "safe, permanent disposal" would be as simple as dumping it into the ocean and making sure it mixed up.
After a couple of hundred years it's no more radioactive than the ore from which it came.
Anyone who pulls the "long half-life" ploy doesn't know what they're talking about.
Long half-life = less radioactive. By definition.
I mean, you do know that "half-life of infinity" is the same thing as "not radioactive at all", right?
Somewhere out of the way then would be like the Sahara, which not coincidentally, is still out of the way; and desert regions are also where it's usually proposed to store waste.
Today we could be reducing the volume of HLW if the US deployed pyroprocessing and cadmium distillation. Unfortunately for the USA, those technologies are more mature in Korea.
At current energy rates & waste production rates etc, if you used only nuclear power, your consumption would result in roughly 7 lbs of nuclear waste over an 80 year lifespan.