Of the two shopping centres in town, the La Marea centre by the main roundabout is newer and has a Supercor supermarket and a few fashion stores. The Ancora shopping centre, by the Whale Tail roundabout, is older and caters to tourists and expats. It has restaurants, Scandie bars like Rock & Troll, and stalls selling fresh fruit and veg.
Arguineguín's local shops are dotted throughout the town between the main GC 500 road and the sea. Some haven't changed for 50 years while others are moving with the times. If you're looking for something specific you're best off asking in a cafe rather than trying to find the right shop.
Most of the shopping that happens in Arguineguín is at the big outdoor market every Tuesday. This fills the car park at the east end of town and is wildly popular with visitors from the resorts. Arrive early to avoid the crowds.
Boutique Tere is a good place to look for clothes, but your choice in Arguineguín is limited and you'll probably need to read our guide to clothes shopping in Gran Canaria if you are up for a serious shopping day.