If that grocery sells products made in Turkey, no Armenian will shop there - per our Armenian friends.
Love H Mart for Soy Sauces and noodles that you cannot find in standard supermarkets. Had a favorite Mexican market in the old neighborhood where I could get various varieties of dried beans, including a wonderful little red bean from El Salvador. Discovered great prices on things like pistachios and chutneys at Patel’s. And there’s a fabulous Mediterranean market that dispenses olive oils, cheeses, nuts and spices of all sorts. Took a tour of Mario Batali’s new “Eataly” market a while back. It’s too pricey for me.
DC area (and NE in general) has seen growth of Asian markets for the past 20 years. Within a 10 mile radius of my house I have H-mart (two of them), Lotte (two of them, one of them a huge Costco size store), two Chinese markets, a few Latino markets, and assorted little Vietnamese, Korean, Indian/Pakistani, and Persian groceries. Even the Costco near us is now stocking more and more Asian food items.