Actually, no. The reactor designs in use generate very little waste, just spent fuel rods that have to be kept in safe storage until their radioactivity level goes down to something reasonable. That doesn't take decades, either. The big problem with nuclear waste is the waste from weapons production, and people don't differentiate just like they don't for reactors vs. bombs.
However, long term interment isn't what's planned anyway... the fuel rods can be reprocessed into new fuel, and they aren't much of a storage concern anyway... they can actually be stuck on a truck and hauled away in their casks down the highway.
We need somewhere to store the fuel assemblies that's safe and secure (or better than putting them in casks in the open) but we're not looking for a dump site. More like a warehouse facility, where they can sit until reprocessed or dismantled.
Coal : Effect/Pros - Energy/Cheap. Residue/Cons - C02/GlobalWarming
Nuclear : Effect/Pros - Energy/Clean. Residue/Cons - RadioactiveWaste/Contamination.
Where do the nuclear byproducts go currently ? Into the earth? Rivers? Oceans?
30 years ago, we switched from paper based products to plastic, to save trees. Today, we want to switch from plastic based products to paper, to avoid pollution.
Every 'switch' will come with side-effects that the current generation is fine with, because they're not going to be ones dealing with it.
No where, because there aren't any. If you meant spent fuel if it's not reprocessed it's stored as long as needed to be less dangerously radioactive. If it's reprocessed, any radioactive elements in it that aren't useful are stored and left to decay. Present storage of things like this is on-site as mentioned above, because reprocessing mostly doesn't happen.
The amount of unusable material from reprocessed fuel is tiny, by the way.... even less trouble than storing the spent fuel rods, on the order of a handful of material from a whole fuel rod assembly.
Power generating reactors don't give off anything but electricity, heat, and spent fuel, they are zero emissions.
Obviously, capitalism isn't very good at accounting for externalities, whether they are measured in birth defects, or in degrees centigrade - but I think global warming is a bit more extreme in scale than your typical pollution issue.
Gen III/III+ conventional reactors were also claimed to be cheaper to build. Look how that turned out.