I'm going to assume I don't need to explain what tempura is to you, given that it might be the most ubiquitous Japanese dish. But you may not know that this emblematic dish made its way to Japan via the Portuguese!
A few reliable Asian food sources in the New York area:
- in Flushing:
... HMart: Korean food: 3 locations on Union Street and Northern Boulevard http://www.hmart.com/company_new/shop_main.asp
- in Westchester:
-- White Plains
... Kamsen Asian Market, Korean and general Asian (China, Japan, Philippine, India, Thailand)& Latin American in the Mall in White Plains 22 Barker Ave, White Plains NY 10601 http://kamsenfoods.com/
... Daido Japanese Market, in White Plains 522 MAMARONECK AVENUE WHITE PLAINS, NY 10605 http://daidomarket.com/