Loro Parque is a fantasy wildlife park located in Puerto de la Cruz, so a bit of a drive from the South but well worth it. Whales, Dolphins, Apes, and even Penguins. Discounts for local residents.

Mount Teide. No visit to Tenerife is complete without a visit to Teide. You can just visit the Cañadas, the mountain range below the crater, or you can take a cable car to just below the crater. If you want to walk up to the crater itself, you have to get prior permission, see the website above.

Botanical Gardens - Jardín de aclimatación. The botanic gardens in Puerto de la Cruz are small but perfectly formed. Established 300 years ago, they were used to aclimatise plants brought back from South America before they were then used in mainland Spain.  If you are going to Puerto, they are well worth a visit.