In the U.S., I go to Trader Joe’s, which is available in 30+ states. Wegmans on the East Coast.
Cost Plus World Market is nationwide in the U.S. and terrific for treats, wines, tea, coffee and other foodstuffs from internationally, at reasonable prices. For example, there are loads of U.K./Scottish brands, like Tunnock’s and McVities. Crave mincemeat pies at Christmas, British teas, etc.? World Market has robust selections. They ship, but the stores have much greater inventory.
I rarely go grocery shopping in person. Instead, I usually order via DoorDash, Instacart and such apps. Or via the specific store’s app.
Like in Asia, I use Grab, which delivers restaurant meals, groceries and much more. In China, Meituan.
In the U.K./Scotland, I use Deliveroo. I also order there directly from Waitrose and Marks & Spencer. You can even have wine and liquor and some sundries delivered, which I use as gifts for folks back home.
It helps to get info from hosts as well. Like I’m going to sit in NYC soon and my host says they’ll have delivery menus and recommendations ready for me, because there are many restaurants that deliver independently in their area.
In NYC, there are also upscale specialty grocery stores, independents, like these: The Best Gourmet Food Markets in New York — Feenster .
Across the U.S., there also are many Asian chain supermarkets, like H Mart and 99 Ranch, which are prevalent in states with concentrations of Asian-Americans (both coasts, parts of the Midwest, Texas and Georgia, for example). H Mart is also available via the Instacart app. And if you have a Costco membership, that’s also available via Instacart.
Also across the U.S., you can find Chinatowns in many cities. And in places like San Francisco, there are other neighborhoods with concentrations of Chinese shopping areas, like Irving. In New York, Flushing has loads of blocks of Chinese restaurants, food courts, markets and other shops. Great eats from across China at good prices, because of intense competition.
In Canada, large concentrations of Asian supermarkets and restaurants are available in Vancouver, Richmond and Toronto. That includes some malls/strip malls with nothing but Chinese businesses.
I often use grocery/restaurant apps when at home, when sitting and when staying in hotels. The apps are useful even ahead of your visits or sits, because you can check what’s available in the neighborhood nationwide or globally — just change the delivery address and you’ll see whether they cover the area and what’s deliverable.
You don’t even have to buy via apps to use the apps to do reconnaissance. Like I’ve sat for folks and found restaurants they didn’t even know about in their area, which they asked me to recommend to them. 
On the food delivery/grocery apps, you can even search for a specific dish, say I feel like some beef rendang or empanadas or pho. And no matter where I go in the U.S. West Coast, I search for Guamanian food. For that, I also use Yelp. In the U.K./Scotland, I search for full English or Scottish breakfasts and often get them delivered. In Glasgow, I found a place that delivered breakfast, as well as Tunnock’s wafer bars by the dozens, so I didn’t have to run around. (Though now I can find them near my home, thanks to Cost Plus World Market.)
Personally, I don’t sit anywhere without good restaurants and grocery/meal delivery. And when I do road trips in the U.S., I use an app called iExit, which highlights restaurants, coffee shops, parks, gas stations, etc., right off whatever freeway/highway you’re on, so you don’t need to wander far if you don’t want to.
If you’re traveling and want recommendations, social media usually has robust, fresh offerings. If you search on such platforms and start consuming/liking such content, the algorithms will start pushing more and more toward you. Like I save content for various countries, states or such, for when I visit.
For example, I found out about T&T openings in the Seattle and San Francisco Bay Area via social media. It’s a Canada-based Chinese grocery chain that’s phenomenal. It’s the best Asian grocery store ever, including selling Peking duck kits, ready to eat, in their hot food area.
If you’re ever in Ohio, this supermarket is overwhelming, goes on for blocks: https://junglejims.com.
If you’re in Texas, H-E-B supermarkets are amazing. Lots of terrific in-house products that hook people. One recent social media post showed a traveler carrying 70 packets of H-E-B tortillas to take back home. 
