Costco – Leicester – Opening Hours & Store Details Costco is directly located at 3 Westmoreland Ave, a 3.77 mile driving distance north-east of the centre of Leicester, in Thurmaston (close to Murphys Lake and Birstall Nature Reserve). The store is an outstanding addition to the local businesses of Thurmaston, Syston, Wanlip, Rushey Mead, Barkby, Orchard Mobile Home Park and Birstall. This page will provide you with all the information you need on Costco Leicester, including the opening hours, store address info, customer reviews and other beneficial info.