In Melb.Aus, it was “Northlands”, when I lived over there, even though Northland was obviously not a persons name.
“Supermarket” in my family here, although the companies never use that word or any other generic term: they’d far prefer me to commit to shopping at a particular name.
I’ve lived in the midwest for ten years adn I still call it going to Wegman’s (or familiarly Weggum’s) The little plastic bags you put the items in to carry them home are known as Weggum’s bags. My wife, born and raised in the midwest, has no concept.
Grocery store or supermarket, or by the store’s name (I’m off to the Acme/Sainsburys whatever).
Mr Boods just uses the store’s name.
My mother used the name of the store that had stood on that spot in 1950, despite it now being 2014 and several, different grocery stores later. God help you if you need to get driving directions from her, as you’ll have to have a complete working knowledge of all of the former street and place names going back several decades.
Come to think of it, I’ve been calling the Macys in the Christiana Mall, DE, ‘Bambergers’ since about 1977.
They’re all in northern Delaware, too – we got our bread and deli meat from them. The name baffled the fuck out of Mr Boods when he first came to visit, but not as much as Happy Harrys and Acme did (‘WTF’ for the former, and ‘Do they sell anvils to coyotes?’ for the latter).
(If I say ‘I’m going up to the store’ to Mr Boods he assumes I mean London. :D)
When I lived in Philly (Landsdowne, actually) I shopped at Pathmark in Upper Darby. The Acme was a little closer, but the name was too weird. Plus, native Philadelphians pronounced it Ac-a-me.
The grocery store (“I’m going to the grocery store.”)
“The store” (“I’m going to the store.”)
Store’s proper name (“I’m going to Safeway.”)
“Shopping” (“I’m going shopping.”)
“I’m going to the store” is probably the most common thing I’ll say. But also “the grocer” or “the grocery” or “the market” or “the supermarket” or by name. Right now, we live so close to a Ralphs that we’d both know that’s where I meant.
“I’m off to the shops” if I’m going to more than one, not sure what I want, am being deliberately obtuse or I can’t be bothered to name it/them all. “I’m going to <shop name>” if I think the person I’m speaking to will also want to go, they might need something from there or I want to be clear that I’m only going there and don’t anticipate wanting to wait around a women’s clothes shop for half an hour while they look at blouses.
I knew someone stationed in Fayetteville, North Carolina who would take his wife on a northern Virginia weekend simply to revel in the wonderfulness of Wegmans. I saw a tour bus take people to visit the Wegman’s flagship store in Pittsford, NY. My own Wegman’s in Ithaca is good, but I enjoy visiting the bigger ones in Dewitt (just outside of Syracuse), Binghamton, and Rochester area. I pity you folks in that burg downstate on the Hudson, because you do not have the wonder and glory that is Wegmans.