Arguineguín market is one of the big three in south Gran Canaria along with Mogán and San Fernando and fills the town every Tuesday morning. The stalls are all along the seafront on the cement factory side of town.
Most stall holders at Arguineguín also work the Puerto Mogán and San Fernando markets so there isn't much on sale that you only find at Arguineguín. That said, you can buy everything from silver jewelry to African baskets and it's a great day out. Look out for the smoothie stand at the south end of the market.
Getting to Arguineguin on a Tuesday is tricky if you leave it late as the buses and ferries are often full. Parking is a nightmare so consider hopping in a taxi rather than driving.
Avoid the crowded restaurants on the market side of town by heading back towards the beach for food. There's a string of restaurants facing the beach, including the excellent Taste Mesón.