Costa Coffee – Elgin – Opening Hours & Store Details Costa Coffee occupies an ideal site at 66-68 High Street, approximately a 0.18 mile driving distance east from the centre of Elgin (near to Moray College and Cooper Park). The store serves the customers of Moray Street, Pitgaveny Cottages, Gleneagles Drive, Bishopmill, Elgin Town Centre, Pitgaveny House, New Elgin and Findrassie. On this page, you’ll find store hours, location details, email contact and other information about Costa Coffee Elgin.