Costco – Reading – Opening Hours & Store Details Visit Costco at 100 S Oak Way, approximately a 2.34 mile driving distance south of the centre of Reading (not far from Costco Mall and Madejski Stadium). The store is an important addition to the locales of Whitley, Ryeish Green, Shinfield, Church, Kennet Island, Mereoak Park, Grazeley Green and Three Mile Cross. Here you may find the specifics for Costco Reading, including the opening times, directions, direct telephone and more important information.