The local farmer's market in nearby Playa de San Juan gives you a taste of un-touristy shopping. Farmers markets were set up a few years ago by the government to offer local farm produce at bargain prices so you'll see plenty of locals stocking up on fish and fruit and veg that is grown in abundance on the isle.
For great clothes, capital Santa Cruz cannot be beaten. Head down Calle de la Castilla for cut-price Zara, Mango, Quiksilver and Massimo Dutti, or head to classy department store El Corte Ingles on El Pilar. If you don't fancy visiting the capital, Costa Adeje and Playa de las Americas also have some upmarket shopping malls.
You won't find any particular attractions in La Arena, but there are a number of theme parks in the Playa de las Americas area. Visit the water park Aqualand in Costa Adeje, or Las Aguilas in Los Cristianos.
Further afield, but worth the journey is Loro Parque, Tenerife's biggest tourist attraction. Orca whales and dolphins jump on command and there are over 350 species of parrot to chat to.