Markets
Super markets
CenturyMart
Newest three-story hypermall: 1) department store, 2) grocery, 3) household goods. Decent section of foreign foods: Walkers Shortbread, Lindt and Toblerone chocolate, olive oils, wine, etc.--even Chinese versions of Spam! More orderly grocery area than Carrefour. CenturyMart card gets you slight discount, but not required.
Department stores
As a foreigner, you can exchange your money at all major banks. A maybe wiser alternative is to use your foreign debit card. International ATMs Plus/Maestro can give about ¥2,500 about 250,- Euros out of each ATM at every transaction, up to a total maximum of ¥5,000 each day depending on your bank, which should be sufficient. International ATMs can be found all over the place and often have an English language option available before you insert your card.