The current advice for avoiding the possibility of exposure to radiation from the Fukushima Daiichi nuclear power station is to stay outside the 30km exclusion zone. Some foreign governments are saying make that 80km, just to be doubly safe. Yonezawa is just over 100kms from the plant as the crow flies, and is on the other side of the mountain range which runs down the spine of northern Honshu giving further protection.
The exclusion zone is to prevent people from making contact with radioactive material that has already fallen. As i understand it from news reports, the stricken plant is NOT pouring out plumes of radioactive material anymore, so it's unlikely any significant amount of new material is settling on the ground (especially not beyond the plant gates anyway)
Even at the height of the crisis there were no evacuations from the western side of the island (where you'll be going), and things have certainly improved further since then.
As I've said to other Nomads, large doses of radiation over a short time are harmful, so are small doses over a long time. I take it you'll be in an area which has very low levels of radiation (if any at all above normal) and you'll be there for a short time, so the risk is significantly reduced.
I'm not a scientist, but personally I think the risk of exposure is very slightly higher, but absolutely nowhere near exceeding safe or normal levels.
It's up to individuals to make their own decisions on what is an acceptable risk, I just hope I've helped you with some sensible, non-alarmist information. almost 7 years ago