I lived 6 miles from an operating nuclear power plant for decades. It was fine. Interestingly, the most pro-nuclear people are often those who live in the emergency planning zone. It's thought that this is due to the local outreach that the plants do with boy scouts and whatnot.
That's also certainly part of it. I think it's a good thing that people who work there generally feel very safe. Interestingly, the nuclear industry has one of the best occupational health records. Mostly because you have to take a damned training before you operate a ladder.