Canary Island culture is actually as distinct from Spain as Hawaii is from the rest of United States, and many Europeans travel to the islands for their year round delightful mild climate. The name actually comes from the local breed of dogs (canes), not from the bird species of canaries, and was once known as the last stop on any voyage from Europe to the New World across the Atlantic Ocean.
I would recommend visits to the markets in Tenerife followed by a visit to one of the many excellent fish restaurants where you can get some tasty fresh seafood perfectly accompanied by the local wines. For a great local experience, go to Tenerife at the end of January to experience the carnival, then rent a car if you want to get away from the massive amounts of tourists, and drive up to the northwestern part of the island for wine growing mountain terraces in Tacoronte-Acentejo, where vines grow at altitudes up to 1000 meters.
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