Puerto de la Cruz is not a major shopping centre but you'll find lots of small independent stores in town selling fruit and vegetables, cakes, jewellery, crafts, souvenirs and fashion. Around Plaza Charco and Calle Quintana stalls sell roasted sugar almonds, candy floss and a range of tempting homemade pastries.
The town hosts regular craft fairs and there's a daily farmer's market on the upper floor of the Mercado Municipal (Avenida Blas Perez Glez; 9am-2.30pm) and an excellent weekly farmer's market at nearby Tacoronte (Calle Tacoronte-Tejina, San Juan; Sat-Sun 9am-2pm).
Head to the Martiánez Commercial Centre for clothes (Stradivarius is great for fashion), shoes (look out for Carolina Boix - sexy shoes at rock bottom prices), music, crafts and a hypermarket for food, booze, cigarettes and household goods.
The best of the shopping is out of town at the La Villa commercial centre (a 10 to 15-minute taxi ride) where they have all the main Spanish stores and the Al Campo hypermarket.
Puerto de la Cruz is in Tenerife. For general advice on shopping in Tenerife, see my Shopping in Tenerife page.