Argos – Billingham – Opening Hours & Store Details You may visit Argos in Billingham Town Shopping Centre on The Causeway, approximately a 2.97 mile drive north-east of the centre of Stockton-on-Tees, in Billingham (near Billingham Golf Club and John Whitehead Park). The store is an important addition to the districts of Elwick, Cowpen Bewley, Newton Bewley, Billingham, Wolviston Court, Wynyard Village and Sedgefield. Here you will find some pertinent information about Argos Billingham, including the business hours, directions and email address.