General tips & Everyday purchases
Everyday spending is a large part of a monthly budget. References and link appearing here should offer significant value.
Kakaku is a price comparison website with extensive coverage. It can also be used as a reference to negotiate down prices in actual stores.
Keepa is a free price tracking add-on for Amazon that works for Amazon Japan. Once installed, it will automatically an interactive price history graph on amazon pages. It has tracking capacities.
New vs used
Used offers significant discount against new while quality can often be high. Yahoo auctions, Mercari and jmty are some of the most popular option. Note that Jmty is also a giveaway side, and does not participate in the transaction- meaning less protection but no fee. On the other end, buying from brick and mortar secondhand stores like Hard-Off, Book-Off, 2nd Street, or Sofmap may cost you a bit more than online marketplaces, but goods purchased from these stores will come with a warranty (shorter than manufacturer original, but more than you'd probably get from a Yahoo Auctions or Mercari seller), and on the flip side, you can sell to them and receive cash payment straight away instead of having to wait for your item to sell.
Utilities
About choosing cheap utility providers
Everyday purchases
If you're the type to pay cash or debit most places, you can look into buying vouchers at discount ticket shops (金券ショップ) for your daily spending (grocery stores, restaurants, conbini, postage, even train and bus fare depending on the operator and store you're buying from) and save a few percent that way. Most chain stores offer these vouchers as a shareholder benefit, but people who would rather have cash will sell their vouchers at a discount to these ticket shops. Most vouchers are specific to one chain or to all chains under one corporate holding company (for example, a Yoshinoya voucher can be used at Hanamaru Udon), but some are usable at multiple different stores.
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Tosho Card NEXT- can be used to purchase books at most physical bookstores
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QUO Card- can be used at any conbini for purchases of items (not for buying other prepaid cards or bill payments)
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Orange Card- essentially a JR gift card, can be used to purchase fare tickets at JR ticket machines or pay fare differences at fare adjustment machines. An Orange Card from any JR company or JNR/国鉄 can be used at any other JR company's ticket machines so long as they support Orange Cards, and the largest discounts (3-5%) are on 1000-yen cards.
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JCB or VJA gift certificates- can be used at a variety of stores, check here for JCB and here for VJA. Note that depending on where you buy these, the savings here isn't as great as with the store-specific vouchers because they're so widely accepted; expect to only save 1-2% (sometimes 3%) using one of these vouchers (with store-specific vouchers, savings can be as high as 10%).
Food
Certain Lawson stores have an in-store kitchen, with an accompanying separate bento and fried food section (the way to tell is that food made in-store is displayed at room temperature instead of in the cold section). These items are typically discounted in mid to late afternoon (4-5pm). How much items are discounted varies by store, however, and the fact that these are displayed at room temperature may be off-putting to some.
Groceries
Supermarkets usually offer discounts up to half price on fresh food at a certain time, usually before closing down for the day. Look for a sticker with a percentage or 半額 (the kanji for "half price") on the item indicating how much it's been discounted.
Gyomu Super has competitive prices and a large selection of frozen goods, as well as import food.
Specific food
Butcher :
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Hanamasa 肉のハナマサ in Kanto
Import/foreign food
About sourcing Mexican food & ingredients
Sellers with stock in Japan, and retail locations :
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Kaldi Coffee, alcohol, and a relatively large assortment of import food
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Jupiter Coffee Similar to Kaldi
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Seijo Ishi assortment of import food
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Yamaya Primarily focused on alcohol, but also has an assortment of import food
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Liquor Mountain Similar to Yamaya
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Gyomu Super has an assortment of import food, usually with competitive prices
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costco Large assortment of american and world food, needs paid membership
Sellers with stock in Japan, and online only :
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Wholemeat.jp - import meat
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The Meat guy - import meat
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Dress Table - European food (italian/french/spanish cheese, italian ham, foie gras ...)
Sellers outside Japan