To put it simply, even if you ate nothing but food from borderline contaminated areas - for the length of time I imagine you will be in Japan, you would suffer no ill effects.
However, if you plan on living in the exclusion area, picking food growing at the side of the road and eating it without so much as washing it... You should be worried.
You say you will be in Kyoto. Kyoto has received no damage nor has it shown any rises in radiation. It is so incredibly far away from the reactors that there is no way it could be in the water. Food sold in Japan is a mix of food from all over the country and from outside Japan. I would be more worried about buying cheap produce from China than I would be about possibly getting a microscopic amount of contamination occasionally via food.