Cueva del Viento is the serious sight above Icod: a long volcanic tube formed by lava from Pico Viejo, next to Teide. The cave is not a show cave with coloured lights. It is a guided walk into Tenerife's volcanic plumbing, with rough floors, dark passages, and explanations of how the island was built.
Book ahead, wear proper shoes, and bring long trousers even when the coast is hot. The visitor centre is outside the town centre, so plan the transport before you commit to a tour time.