Trujillo has a large local shoe making industry. Venture down to the shopping district, in and around Pizarro road and Ayacucho Road and pick up some hand made beautiful leather shoes.
Other leather goods, woodcarvings & replicas of Precolombian ceramics in the beautiful old colonial centre and at archaeological sites.
If you ignore culture and cannot live without modern brands:
Mall Aventura Plaza: On the way from Trujillo to Huanchaco. A supermarket "Tottus", 2 department stores Saga Falabella and Ripley, a Food Court MacDonalds, KFC, etc., Cinemark, banks, atms, and many other stores can be found here.
Real Plaza Trujillo: Starbucks, KFC, Pizza Hut, etc. Supermarket: Plaza Vea, Cineplanet, etc.