This, this, this. A million times over. Humans are really bad at estimating real risk, are even worse at comprehending scale, and tend to fear the exotic or unknown. Nuclear power gets the triple whammy here.
Real Risk: The health/death risk of Nuclear power to the public is so vanishingly small it disappears on any graph you can create. There have been 9 or 10 deaths in the 60 odd years of civilian nuclear energy in the US. None by radiation. About half by electrocution ( they are electric plants... ) and the half by physical events, pressure explosions, heavy things falling.
Scale: 100 Nuclear power plants have produced about 20% of the entire US electric grid for the past 60 years. In contrast, 600 coal plants produce about 40% of our needs. On top of that each coal plant needs a constant supply of coal, and much more land to operate. The land use efficiency of Nuclear is much, much better. As far as the Nuclear waste argument, here again, failing at comprehending scale. The spent fuel rods consumed for the past 60 years of nuclear power would fit into a single house.
I would like to give some credit where credit is due, and where reasonable regulations apply. Airliners are extremely safe because of the NTSB doing amazing work, getting to the bottom of every major crash and then back feeding that information into actionable fixes. The same goes for the NRC. I am hugely pro-nuclear power, but also believe the NRC is an important part of that environment.