Costco – Birmingham – Opening Hours & Store Details Costco is directly at 100 Watson Rd, 1.92 miles north-east of the centre of Birmingham, in Nechells (next to Junction 6 (Gravelly Hill Interchange) of M6). This store is situated in a convenient location to serve the customers of Stockland Green, Gravelly Hill, Ward End, Saltley, Washwood Heath, Erdington, Nechells and Aston. This page includes working hours, place of business address and telephone number for Costco Birmingham.