La Palma is a popular hiking destination as much as a popular sun destination. You may like both, and take advantage of the very good flight connections to the island. Most prominent feature is the huge erosion crater, Caldera de Taburiente, a National Park. Highest summit here is the Roque de la Muchachos, 2426 m.
The long side of the pear shaped island points to the south. This is where volcanic features are found which can be explored on foot; just follow the GR131 marked trail. By the way: this trail is also part of the European Long Distance Path E7.
The other GR on the island is the GR130, a circular walk around the island, more level than the GR130, connecting a series of villages.
In addition to the spectacular rocky mountainous center of the island, with its volcanoes and craters, the forests in the north and northeast are a second must-see. The trade winds from the north hit the island, the air is lifted, causing a zone of semi-perpetual clouds and mist. The green moist forests with large ferns and evergreen laurel trees, often hidden in steep ravines, are an oasis compared to the dry south. We mentioned the two GR's on the island. Apart from these, many regional or local routes, well-marked, give you the opportunity to explore these micro biotopes such as the steep barrancas on the north coast or the string of volcanoes on the south crest.
Check the complete list of Canary Islands.