With low budget, it is very hard to find decent restaurants and food stuff, but here are some tips that I have.
Amongst fast food, there are few chains where workers are able to provide you info about their food and where they were produced.
- Mos Burger (most workers are very used to be asked questions and show sympathy with your concerns) - Freshness Burger (have some goodies like miso onion burger, and could modify vegan stuff very easily) - Denny's (They could even show you a meal package to let you see what it is. They are not as racists as US Denny's. The workers told me that they have decreased the number of meals on the menu because they prioritize to provide stably checked food)
I personally think that Fukushima is not the only definitely-to-be-avoided since the radioactive incineration is happening even in South East Japan.