Since there is no electricity, wouldn't all the nuclear reactors around the country be down and already released radiation into the air? Why is there no sign of this?
Most modern reactors use what might be termed Passive Safety measures. In other words, if not tended to, their components are built to quench the reaction rather than to sustain it. The method for doing this varies, but you can find several examples in the link above. Older reactors, of course, were more prone to runaway reactions, and some modern cases of nuclear failures, including Three Mile Island Unit 2, had such passive safety measures in place, but suffered failures that prevented them from working properly.
Ultimately, of course, even reactors that worked properly would eventually lead to ecological disasters as water, wind, and plant roots eroded away protection metal and concrete, releasing the radioactive material, but it would take much longer.
The government would attempt to keep any power plant running as long as feasible. Especially a Nuclear power plant, due to the added complexity. Nuclear power plants are generally self-sufficent, and could run a long time baring critical failures. If something, like the plague, required abandoning a power plant, you know that it will not just be left operational. It will be properly shut down, and likely made inaccessible through normal means. Obviously, the government does have failsafes in place, like the CDC building's
high-impulse thermobaric (HIT's) fuel-air explosivesused for decontamination when the building runs out of power.
Atlanta is not close to any nuclear power plants. The two in Georgia are many miles east and south east of Atlanta. The closest in Alabama is North West of Atlanta. In any case of nuclear radiation/fallout from a plant, wind patterns will not direct any towards Atlanta.
Radiation effects quickly decrease due to distance. Atlanta is too far from any of the surrounding plants that even if they were in the right spot for the wind to deposit fallout near Atlanta, it would be minimal.
The meltdown at three mile island is a good example of passive safety. The operators there actually KEPT water out of the core because they were reading a faulty indicator.
Eventually more than 1/3 of the core melted down, the melted down fuel and containment (called corium) flowed into the plenum and fission stopped. In order to keep fission going in a nuclear power plant you have to keep the fuel "close together" in order to maintain criticality (or "burning"). When enough of it melts away there isn't enough to maintain the reaction. There WAS a release of radiation, but it was vanishingly small. I believe the NRC finally estimated that 2 million people got about a millirem of exposure. In perspective a chest x-ray is 6 milirem.
As far as the long term issue of the building and containment eventually being worn away, as long as you didn't eat or inhale the actinides you'd be fine. Alpha and beta decays from the nuclear fuel are stopped by millimeters of air, or even a sheet of paper.
Having read the comics and watched the show almost obsessively, I think the answer is relatively simple:
The survivors, especially in the comics, wouldn't notice any possible radiation leaks. For starters, they obviously have more important things to deal with, like zombies, cannibals, sociopathic community leaders (like the Governor), psychotic bandits (like Negan), and, prior to their arrival at the Alexandria Safe Zone, they were facing many other threats of a more insidious nature, such as starvation, dehydration, exposure to the elements, injury/illness/disease with no access to medical care, lack of ammunition, and so on.
Until Rick's group reached Alexandria, they barely had time to think about anything other than basic survival. When you are hungry, thirsty, homeless, surrounded by man eating corpses, and being hunted down like animals, you aren't going to spend a lot of your time worrying about things as uncontrollable as nuclear reactors. You'd probably be happy to live long enough to develop cancer from a radiation leak - but you almost certainly wouldn't expect to get that opportunity.
These people are just trying to live to see the next day, and the harmful effects of long term exposure to radiation is probably the farthest thing from their minds. The only person in the group who might be able to use a giger counter properly is Eugene, and before they got to Alexandria, he was in the doghouse for lying about being an epidemiologist with the solution to the zombie problem. And even if they somehow managed to find a giger counter, the batteries required to operate it would be put to better use in a flashlight, radio, or some other device which would be more beneficial in the short term.
Once the group arrives at Alexandria, they have finally found a veritable Garden of Eden, and I don't think they would be inclined to leave it for anything short of an attack by a dragon or something equally catastrophic.
If they did somehow discover that there was a substantial amount of radiation in the area, they would probably weigh their options, which are quite limited. I think they would eventually come to the conclusion that a safe haven with enormous, well defended walls, plenty of potable water, access to food, medical personnel, and a large number of good, trustworthy people who are committed to the defense of their new home, is such a valuable asset that the presence of ambient radiation isn't a big enough problem to justify abandoning the place.
These people aren't living in our world. They are living in an endless nightmare, and Alexandria is the first good thing to happen to them since the world fell apart. They are safer there than they have been anywhere else so far, and that kind of safety isn't something that should be taken lightly, and it certainly shouldn't be thrown away lightly either.
You have to remember that the survivors don't have the same kind of expectations that you or I do in our pleasantly pre-apocalyptic world. Most of us assume that we will live long, relatively healthy and happy lives, and eventually die of old age at some point in the distant future.
The characters in The Walking Dead, on the other hand, don't expect to live long lives, although their expectations were probably drastically improved when they found the Alexandria Safe Zone. Still, they don't take anything for granted, especially longevity, which is almost unimaginable to them, despite the relative security they've attained by fortifying the community.
It has taken these folks a very long time to build up everything they now enjoy having. They created a stronghold with robust walls, full of life saving supplies, inhabited by a large number of generally decent and trustworthy friends, neighbors, and leaders, and a community of people who are devoted to one another and to keeping the things they've invested so much time, effort, and blood into building and maintaining.
If they shared our expectations, values, and priorities, they might be willing to leave Alexandria if they discovered that there was a significant amount of radiation in the area. But they don't share our expectations, values, and priorities. They're dreams probably include things like living long enough to have to worry about things like radiation. Their actual lives are such that they probably don't expect to live long enough to worry about it, though. They're just happy to wake up each morning and live through the day.
And more to the point, as I said earlier, we have no reason to believe that they have even considered the potential threat of radiation leaks. It just isn't something that would be likely to cross their minds. They have spent the last several years (about 4 or 5 years in the comics, and maybe 2 years on the show) trying not to be devoured by zombies, murdered by sociopaths, or eaten by cannibals. When they weren't actively fighting off these threats, they were desperately trying to find food, water, and shelter. These were their priorities, and they were absolutely correct to set them as their priorities.
The amount of radiation they might be expected to encounter would take years to kill them. The average lifespan of characters in The Walking Dead, from their first appearance to their deaths, is probably around 6 months, maybe a bit less, maybe a bit more.
A brief timeline of each character's lifespan:
In the comics,
The only people who have been around since the beginning are Rick, Carl, Sophia, and Andrea. Maggie and Michonne joined the group a short time later, and they, too, are still alive. Abraham, Eugene, and Rosita first appeared about halfway through the series, and of these, Abraham died, probably about a year after he showed up. Glenn lived for a couple of years. Lori lived for less than a year. Amy died almost as soon as she first appeared. Judy was killed while she was still an infant. Herschel was around for a few months. Dale lasted maybe a year.
On the show,
The only people who have been around since the beginning are Rick, Carl, Glenn, Carol, and Daryl. From the farm, only Maggie is still alive. From the prison, Michonne is the lone survivor. From the Governor's group, only Tara and Sasha remain. Andrea lasted a year or so. Herschel made it for a year and a half. Lori survived for a month or two longer than Herschel. Amy lasted a few days. Shan lived for a couple of months. Merle made it a year. Sophia died after a couple of weeks. And so on.
These lifespans are not long enough to justify worrying about the harmful effects of radiation. And even for the people who have survived the longest, there are far too many other, more immediate dangers to deal with for anyone to think about unknown and largely unknowable threats like that. They need to focus on the bare essentials, like food, water, medicine, and defense from outside enemies, both living and undead.