Atlantic Superstore Sussex weekly PDF Flyer for Lower Cove Road 44 Lower Cove Rd, Sussex, New Brunswick store. Of course Atlantic Superstore is one of the better grocery stores and you can find everything that you may need inside. The employees were super nice, they have a good selection of items, store is clean, prices are good! Some of the produce could have been fresher. Best grocery store in Sussex lots of selection and the staff is great foods always fresh. There's lots of parking, washrooms, flowers, drive thru pharmacy.