I like imported foods myself and to save some money I usually go to Gyomuyo Super or Nikuno Hanamasa. Those supermarkets are a grocery store handling food products not for personal use but for restaurant use. So, the portion of each product is big compared to ordinary products that you buy at regular supermarkets in Japan. BUT the prices are low. They handle many imported products from many countries such as Italy, Spain, China Turkey, Thailand, USA and Canada.
There are many Hanamasa Stores in Tokyo and in the suburbs of Tokyo. Open 24 hours a day. Very convenient!
Gyomuyo Super is originally from Kyogo prefecture in West Japan, and they have chained stores throughout Japan.