I usually start my shopping at Kroger and end up at Ingle's with an every-so-often trip to Aldi for outstanding produce prices. Store brand milk at any store here tends to compete with whatever price Aldi has.
I wouldn't really go to Ingle's if they didn't have the best meat in town (and frequent sales) and great B1G1 deals. If I am going to buy something special like ethnic or organic, Ingle's is a great place to get that as well. The selection is about the best I've seen.
As I am stockpiled well, I only need to buy the great sale items at Kroger. Every week usually has something that is highly competitive, even without a Mega Sale. I don't really care for a lot of their meat, but they run 3 and 4-day sales consistently and have some decent markdowns. They also have some awesome partnerships with manufacturers that allow them to do frequent cereal promotions, etc.
I do go to Target about once a month to pick up the deals which are free or almost free.