Can always stop by a Costco.
I must be honest - this line of thinking was not helpful when we were there a month ago. Yes, you can get stuff, but really NOT MUCH! Chips and nosh, but no real food. Same with 7-11 and all the convenience stores. They have the same food, but now, they manufacture it in Japan, so there is no hechsher on anything being sold. We found a bag of chips at an international store or two - and a box of cereal, that was about it. We made it on fruit, health bars we brought from USA, lunch was sandwiches with tuna or P&J (bread and tuna/P&J from USA), dinner was Channa's place. Not really complaining as much as the outcome to me was we are in the land of pure food decadence, with huge innovation at every street corner.
A drop of effort from the locals would have allowed people to roll into a sushi joint and ask for a mendi (at higher cost) and they would whip on the mendi board, knife and slice a bit of the fish off and boom, sushi rolls, or even sashimi. Sadly, that idea was not well accepted :-( Some of the locals who live there do it, on their own, but no organized apporach.