Here in Minnesota we almost never had national grocery chains. We had a number of large local chains that dominated our grocery scene, in addition to some other smaller ones. We did have Kroger in the 1960s, but this is a very union-oriented state, and someone above mentioned that Kroger does not seem to like that, which may be why they didn't stay.
Our big local chains were Super Valu, Red Owl, Country Club, and Applebaum's. Sid Applebaum is the person that started our current "Rainbow" chain, which was sold to an out of state company in the last year or two, and which I have never cared for. I was surprised to see some Red Owl stores still in operation, though I'm thinking they're just using the name, as I don't think Red Owl has existed as a company for some time now. They and Snyder drug were the same company. Super Valu and Red Owl were headquartered right on the edge of Hopkins, and Country Club in St. Louis Park.
David, you lived right by a Shopper's City! I think that behemoth is still sitting empty up on the hill, at least last I was over there a few years back. You know that building behind SA near Aldrich Arena off White Bear, it was Hillcrest Bank for years, no idea what it is now, that was originally a Kroger.
There was a Shopper's City in Bloomington as well, and some others. They had a separate liquor store (can't have liquor in the main store in Minnesota) and they were interesting stores to a kid, though I doubt I'd ever set foot in one if they existed today. Kind of on par with Kmart or Walmart. They did have a bulk candy counter, and by gum, they bagged your groceries and put them in your car for you!
The St Louis Park Target store, which was the second built, also had a grocery department in its original incarnation. Those grocery units were operated by Applebaum's, who also bagged your groceries and put them in your car. Again, because of the union, the grocery units in places like Target and Shopper's City were completely separate areas in the store with separate cashiers, not "all in one" the way today's super stores are operated. In fact at that time, union grocery stores were closed on Sundays, and I remember the main store being open while the grocery area was closed.
There is a Cub (which started out independent and became part of Super Valu I believe) near my home that I like, probably because it is about half the size (due to limited size of the lot it's built on) of a typical Cub and because I shop late at night. It took the place of an old Super Valu which was demolished to make way for it. I've always gotten fine meats and produce there and they keep it clean and the workers are very nice. I'm much less impressed with the behemoth suburban ones, and find them difficult to navigate. We also have a branch of a small, somewhat upscale chain called Kowalski's not far from here, actually housed in an old Country Club, where I'll occasionally go, particularly if I need something on a weekend when I would never go to one of the mainline stores.
I liked our old line chains pretty much equally, Country Club was known for having good sales (remember the green newspaper sheet ads David?) Red Owl also had a larger, bag your own variant called "Country Store" here for a while which weren't bad stores.
My understanding is that the carpeted, upscale Byerly's, at least in days of yore, were really quite unique in the industry and people are/were quite marveled with them. They are nice stores and I do go occasionally if I'm near one.