Though most Asian supermarkets tend to be neighborhood oriented, small and independent and may carry similar or even identical names, many Asian supermarket nj chains of stores have floor area that is comparable to other American supermarket chain stores. I never get tired of Benihana restaurant. The markets are generally ethnocentric and may be a mainly Asian supermarket nj, Japanese or Filipino market; however, in many areas such supermarkets cater to a more diverse Asian population as a means of financial diversification. Website Directions More Info. Examples include Asian restaurantsbeauty salonsbakeriesforeign film rental storestravel agencies Asian supermarket nj, book storesand other businesses. An Asian supermarket is a category of grocery stores in Western countries that stocks items imported from the multiple countries in EastSouth and Southeast Asia.