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Jardín Botánico / Botanical Garden
Photo: Tetraeder, CC BY-SA 3.0 via Wikimedia Commons
Established in 1788 to acclimatize specimens brought back from the New World on their way to mainland Spain, the small Botanical Gardens have an interesting selection of tropical trees and shrubs. Even if you're not interested, it's a beautiful place to wander around and relax. Don't expect to see much of the native Canarian flora there, though.
© OpenStreetMap contributors
Jardín Sitio Litre / Orchid Garden
The lovely English-style garden of an 18th-century mansion features a large collection of orchids along with bonsai trees and a dragon tree. Famous past visitors have included Sir Richard Burton as well as Agatha Christie, who was inspired to write her short story collection The Mysterious Mr Quin. There is also a pleasant terrace café.
Chapel of St. Telmo
The small chapel was built in 1780 and dedicated to the patron saint of seafarers. After being partly destroyed by flooding in 1826 the chapel was rebuilt, and fully restored several years ago. Of special note is the interior Mudejar-style carved wooden roof truss.
A fantastic, post-modern swimming and sunbathing complex designed by the famous Lanzaroteno architect Cesar Manrique. It's a bit concretey by modern standards but is still an awesome paradise which costs hardly anything to enter for the day. See non-official website for more information.
Park with fountains, waterfalls, and plenty of benches to take a rest in the shade while making your way up the slopes of Puerto de la Cruz. Nice view of the city center.