Like most here, I go to several different places.
I'm at Walmart, 3-4 times a week (family of 6). Sometimes it's grocery pick-up, sometimes I shop, mostly for non-food stuff. I'm not a fan of their produce or meats--the meats, especially, are NOT the best deal in town, and they have a smaller variety, despite being a huge store.
I do a lot of grocery shopping at Aldi's. If you haven't been to one in a few years, it's worth going back--they are always improving. 10 years ago, their produce was shoddy, and most of the meat was frozen or heavily processed (bacon, lunch meat). They have much more, fresh items, organic, gluten-free, etc. While their meat dept. will never rival a regular grocery store--they stick with staples, with the occasional special on lamb or whatever--if you want 90% ground beef or boneless chicken breasts, they have them, and at a good price.
I fill out my shopping with occasional trips to regular grocery stores. Food Lion has low prices and good selection. I find Publix to be pricey, but they have good specials, and their store brands are high quality. I only hit Harris-Teeter (Kroger) for one specific item, and never go to Lowe's.
I'm lucky that I'm spoiled for choice--I have 3 grocery stores within a mile of home, and if you expand that to 3 miles, you could throw in several more, plus Walmart, Dollar Tree (check prices--they have some staples, but not the cheapest), Dollar General, Trader Joe's, Whole Foods, etc.
Interestingly, I had a Sam's Club membership, and considered Costco. They didn't work for me. It may be their location relative to my house--kind of a pain to get to them--but I wasn't saving any money. This may be a "me" problem. I don't buy a lot of name-brand items, so getting, say 500 Clorox wipes was no bargain for me. I know people rave about Costco, so the problem is probably just me.