Shopping in Puerto de Alcudia breaks down into two categories: the resort strip along the waterfront, which sells beach gear, sunglasses, and tourist souvenirs much as you'd expect, and the old town of Alcudia, which has a better range of small independent shops selling food, ceramics, and local products.
The Tuesday and Sunday market in Alcudia is the highlight for most visitors. It spreads through the streets of the old town and is one of the larger markets in northern Mallorca, with a good section devoted to local food produce — olive oil, almonds, cheese, and sobrassada — alongside the clothing and craft stalls. The food section is the part worth prioritising if you're self-catering.