Grocery stores (supermarkets) are open 7 days a week. Some are open 24 hours a day. Below is a list of some of the largest chains you will find in and around Greenville. To figure out the closest one to your home, go to their homepage and click "store locator".
Publix Supermarket: Wide variety of everything you might need, not just groceries, but household goods and cleaning supplies, and lots of other international foods. Pharmacy is on-site.
Whole Foods: highest quality, organic and healthy food, probably the best that you will find but also the most expensive.
Fresh Market: similar to Whole Foods, but less variety.
Harris Teeter: Similar to Publix; food, household goods and cleaning supplies, etc. Pharmacy is on-site.
Costco and Sam's Club: You have to become a member to do your shopping at this wholesale store. They have everything you need (food, some clothes, electronics, etc.). You buy larger quantities, and get a cheaper price. They also have a pharmacy. Open 10:00 to 8:00 p.m.
Trader Joe’s: Good quality food, less variety than Publix and Bi-Lo, no pharmacy.