Travel Mama, as a father I understand your concern, but personally I'd be quite happy taking my two to Kobe. Apart from a 48 hour period on March 16/17(after explosions spread radiation as far south as Tokyo) the radiation exposure has been limited to the area immediately surrounding the Fukushima Daiichi plant. The Japanese authorities say that's 30 km radius, other foreign governments say make it 80 kms just to be safe. Interestingly, if you'd been in Tokyo on the day the radiation peaked, you'd have received a dose roughly equivalent to 1 abdominal x-ray. Since then radiation levels in Tokyo have been normal. Kobe is a further 400+ kms south.
As for food and water: I suspect the water is sourced locally, so is unlikely to be affected by fallout (another note, Tokyo water is monitored regularly and has not shown any signs of contamination).
Food: last week it was revealed that 1500 head of cattle which had been grazing within that 30 km zone around Fukushima had been slaughtered and SOME of the beef made it onto the shelves in Tokyo. Since then all beef from Fukushima has been banned. Plus, a health official said you'd have to have eaten the contaminated beef at every meal for a year for it to reach unacceptable levels in your body.
The thing with radiation is that a large dose over a short time or a small dose over a long time is harmful - if your kids are exposed to any radiation at all, it's likely to be very small, and you'll only be there for a short time. That's my assessment of the risk.... but it is entirely up to you to decide if that's acceptable for you and your family. Hope I've helped.
Phil almost 8 years ago
An update for you all from March 2013
http://safety.worldnomads.com/japan-radiation-study about 6 years ago