Costco – Gateshead – Opening Hours & Store Details Costco is situated within easy reach on Mandela Way,, about a 2.28 mile driving distance west from the centre of Gateshead, in Dunston (a few minutes walk from Handy Drive – Bus Depot Bus Stop). This store is situated in a convenient district that chiefly serves the people of Teams, Spital Tongues, Arthur’s Hill, Whickham, Dunston Hill, Dunston, Elswick and Fellside. Please note the various sections on this page for specifics on Costco Gateshead, including the operating hours, local directions, customer feedback and additional information.