Costco – Leeds – Opening Hours & Store Details Costco occupies a convenient location on Leathley Rd, approximately a 1.13 mile drive south-east from the centre of Leeds, in Hunslet (next to Junction 3 of M621). This store is situated in a convenient location for customers from Leeds City Centre, Lovell Park, Richmond Hill, Beeston Hill, Hunslet, Burmantofts, Holbeck Urban Village and Little London. Please review the specifics on this page for Costco Leeds, including the hours of opening, local map and email address.