Argos – Kilmarnock, Burns Shopping Mall – Opening Hours & Store Details Argos is situated right in Burns Shopping Mall at 18-19 Burns Precinct, about 0.35 miles south-east from the centre of Kilmarnock (in front of The Palace Theatre and Burns Monument). This store is situated fittingly to serve those from the districts of Riccarton, Beansburn, Annandale, Grange, Knockinlaw and Kilmarnock Town Centre. This page will give you all the information you need on Argos Kilmarnock, Burns Shopping Mall, including the opening hours, directions, phone number and other relevant info.