"Irradiated" and "radioactive" are not the same thing. An irradiated sandwich poses absolutely no threat to its consumer.
http://www.fda.gov/Food/ResourcesForYou/Consumers/ucm261680....
So aside from contamination, those sandwiches are likely slightly safer than from other places since the radiation in the area will help sanitise surfaces and foods.
My only concern would be if the water staff used to wash up was contaminated from the soil. But assuming the water is good the food is likely good too.
That said, GP's point is that unless there are radioactive substances flying in the air / otherwise contaminating the store next door, things bought there should be safe. They'll be irradiated (affected by radiation), but not radioactive themselves. Contrary to popular opinion, getting irradiated doesn't cause you to become radioactive.
I'll think rather in a ROG [1] event
[1] Rodent Olympic Games.
Well, actually... Neutron activation and photodisintegration via high energy gamma rays can produce radioactive isotopes via irradiation.
But this generally requires a high flux or high energy to produce noticeable secondary radioactivity. So depending on the type and energy spectrum of the radiation the sandwich is exposed to it might pick up tiny tiny amounts of radioactivity.
But yeah, that's probably going to be drowned out by any kind of radioactive dust.
This would be the place serving the best sparkling donuts in NY probably, and also having the laziest sanitary inspectors in the entire city.