In fact, moderate amounts of radiation are actually good for you.
Nuclear waste is manageable and using nuclear fuel reduces the amount of radioactivity in the world.
I'm pretty sure that's wrong. It's my understanding that the total radioactivity of the waste products exceeds that of the original ore. (This is because the fuel breaks down into decay products that have a shorter half-life, but aren't suitable as reactor fuel.) In any case, we are digging uranium out of the shielding ground and storing its most radioactive fraction in steel drums in populated areas, so the effective radioactivity is increased regardless.