While exploring Eleuthera I have discovered a few stores, working my way from Rock Sound down north, here they are. (NO spell check here...)
3 food stores in Rock Sound. The "Market Place" is the biggest run by the Sands,(closed 1/2 day on Weds, and all day Sunday.) Then there are 2 smaller markets, "Sawyers" (where you can by sodas by the case for $11.90), and "Halls" which has better prices on many items, (romain lettuce is $1.00 cheaper here then at the Market place).
Tarpum Bay has 3 food stores also, "Berts for the Best" has great prices on their meats, and then there's the "Carey's Grocery" next to the Hardware store that often has fresh farm veges: tomato, cabbage, sweet peppers, pumpkin, cucumber, okra, etc. When in season, (the Careys have a large farm just outside of Tarpum Bay) both of these stores are open 6 days a week from 7AM to 8PM, and there's also "Jason Carey's" market, while smaller with fewer selections he sometimes has the better prices and is open 7 days a week, until all hours of the evening. In Palmetto Point the "Island Farm has great salad fixings, depending on the season brocolli, zuccini, beets, cabbage, fresh herbs, basil, cilantro and much more, ( a little pricy but has many things you can't get anywhere else on Eleuthera.), also is "Sands" market at the intersection and several more(4 or 5) small food stores. Governors Harbour has 2, "Burrows" (try Sid's Hell Fire sauce, and be sure to look in those big white freezers), also "Eleuthera Supply" (run the Bethel's, has their own butcher). JC has "Fast & Easy" and just before Rainbow Bay is "Big Rock" ( say hi to Anthony). Hatchet Bay has "Big General" (an interesting place to explore) right next to the liquor store and I belive there are 3 more food stores in the settlement. In Gregory Town is "Thompsons" market and I think a small store across from Pams gift shop. In Lower Bogue there is "Johnsons" Market (where sometimes you can find hot mac and cheese for $1.00 a piece on Sunday mornings), "E & G" food store, and another smaller store between the fruit stands on Queens Hwy. Bluff has a big new store I think it's called the "North Eleuthera" food store, they opened in this past Christmas and there is also "Sawyers" market. In Spanish Wells there is the "Food Faire" (a really big grocery store about the same size of the Market Place in RS), you can find a lot of things here not found in other stores on Eleuthera but the prices are a bit higher here (red bell pepper $7.99 lb, Careys in TB .50 each) there are also 2 smaller food stores here to, but keep in mind the water taxi $5 round trip and if you rent a golf cart it's about $13.00 an hour, if you walk to the Food Faire they will deliver your groceries to the ferry dock for you and you might even catch a free ride back to the boat too!
These are just a few stores that I know of, but there are many gas stations and small shops that also have food items. Happy Shopping!