I'll let you in on some secrets on how we eat well at a fraction of the regular retail price.
Find out where your supermarket's time service corner is. Almost every supermarket I've been to in Japan has a corner dedicated to time service produce and food items. These are products the staff have deemed to have passed their peak freshness or are near expiration. If the supermarket has a corner or a shelf dedicated to these, it is worth visiting it first thing before you roam the aisles as you might already find something from your shopping list there. What I usually do is to go to this section first and plan my meals around what I can get on sale. One time, I found half priced zucchinis, eggplants and orange bell peppers so I roasted these in the oven with olive oil, salt and pepper and tossed them with penne pasta and cheese. We felt like we had dinner at an Italian restaurant.
Fruit is expensive in Japan but necessary for healthy eating else cravings will find satisfaction in cheap snacks that don't have any nutritional value. The time service corner is your best bet for getting them at a great price. I happened to chat with a Japanese woman who was also looking through the time service shelf. She says that the discounted produce in this corner are fresher than the regular priced produce in the US where she used to live. Japanese consumers have high standards on food purchases. Items have to conform to the three Ps: pretty, pristine, and perfect. One wilted leaf, and one dent in a carrot and it's relegated to the time service section.
Supermarkets have their own guidelines when they start marking down food items and it differs per product. At the one I go to frequently, for example, desserts are marked down up to 20% off even on the day of their expiration (probably because people still grab them even at only 20% off) while pickles are marked down to 50% two days before expiration at our supermarket. As you walk through the aisles, train your eye to spot the bright yellow discount stickers that indicate the price off.