You might want to get your camera out and head to El Hierro Biosphere Reserve— just one of the landmarks located 5.2 mi (8.4 km) from central Valverde.
When the beach is calling your name, you might want to head down to Playa de la Arena, located 5.7 mi (9.2 km) from central Valverde. If you want to continue walking by the waves, head to Playa de los Cardones and Las Playas, both within a short walk.
You can spend an afternoon browsing the exhibits at Casa de Las Quinteras Ethnological Center during your travels in Valverde. While you're in the area, stroll along the seaside.
