While the highest point of Spain is Mount Teide, the highest point of the island of La Palma is this strange rock formation that looks like three dudes, called Roque de los Muchachos. There’s a parking area there and a few short, beautiful walks to look out points. It’s also part of many a hiking route. The quickest way to get to the top of the Caldera de Taburiente National Park however, is by car.
According to TripAdvisor, this is one of the best things to do on La Palma. I can second that. The panoramic views over the Caldera and the rest of the island and out to sea are really breathtaking (the islands Tenerife, El Hierro and La Gomera in clear weather as well). It’s a great place to stay for sunset but the drive up and down is really quite long with proper sharp turn and hairpin bends, so be mentally prepared. Here’s a map to the mountain top.
Apart from the normal stunning natural views of the land, scientists and other important people are up there looking at the sky. They’ve made it feel like a trippy sci-fi movie by setting up these massive puzzle-mirrors (telescopes) and named them MAGIC.