I'd suspect the nearest one to much of the trail through MA and southern parts of VT would be the store near Albany (NY) which is certainly not the most convenient but a possibility if one had a day or two (or someone that could transport them, as people often use Albany airport to access the trail for section hikes, and the store is not that far from there).
It definitely conforms to that too little parking thing (even if the building it is in was a small Star supermarket in the 1980's - I doubt they got people from quite as wide a radius as TJ does, though).