Bi-Lo and Food Lion come immediately to mind.
Not familiar with Bi-Lo, but their name suggests the goal.
Food Lion is notorious when it comes to their quality.
For the stores in my locale, we've got:
Super G - where I work, well regarded.
SuperFresh - tries to place itself as high quality, but even after their recent remodel comes across as claustrophobic and uncaring about the customers.
Food Lion - absolutely tiny store.
Safeway - the newcomer in our area, seen as overpriced and not very welcoming.
After nine years, Super G is still regarded as clean and friendly - many people just "visiting" the area are surprised to learn the store is that old. A lot of customers are worried about the remodel we're going through.