La Palma, where it's located

In La Palma, the north-westernmost island of the Canaries, the climate is subtropical oceanic on the coast, that is, very mild and sunny most of the year, with rainfall concentrated in autumn and winter. In inland areas, however, the weather becomes cooler and wetter with increasing altitude; the almost complete absence of plains makes this island moist and verdant compared with other islands of the Canary archipelago. However, on the coast the amount of rain falling in a year is not very high: at the airport, it is equal to 370 millimetres (14.5 inches), most of which occur between October and March, because it is the period when the Canary Islands can be reached by some Atlantic depressions, with a maximum in November and December.
Here is the average precipitation at the airport, located on the east coast, not far from the city of Santa Cruz de La Palma.
La Palma - Average precipitation

On the coasts the temperatures are very mild: highs are around 21/22 °C (70/72 °F) from December to April, and 26/27 °C (79/81 °F) from July to October, as you can see in the following table.
La Palma - Average temperatures
Min (°C)161516161719212121201817
Max (°C)212121222324262627262422
Min (°F)615961616366707070686463
Max (°F)707070727375797981797572

Tazacorte, beach

In inland areas the temperature is naturally lower with increasing altitude: at 600 metres (2,000 feet), the maximum temperatures are on average around 16 °C (61 °F) in winter, and 24/25 °C (75/77 °F) in summer. On inland slopes, rainfall is more abundant as well, and thick forests of pine, laurel and other species are found (in the island there's a large biodiversity).
The prevailing winds, the north-east trade winds, cause haze and cloudiness on the exposed slopes, while they temper the heat along the coasts in summer; they are more intense in the afternoon, being often moderate or even quite strong.
The days of calima, characterized by abnormal heat and light wind, due to warm air masses from Africa, are relatively rare, and are rarer in La Palma than in the eastern islands of the Canaries, given the greater distance from the African continent; however, they are more frequent in spring and summer: in practice these are the only days when the temperature exceeds 30 °C (86 °F), and when the heat is unpleasant. The calima is also felt on the highlands, and often even more than in the plains, because warm air is lighter and tends to rise, while the coasts can be mitigated by the coolness coming from the sea.
The amount of sunshine in La Palma is very good throughout the year, however, in addition to the low pressure systems that may pass during the October to March period, in summer cloud banks can form on the Atlantic and pass over the island, while on the northern coasts, and especially on the mountain slopes exposed to the north, local clouds and fogs can form. The southern coast is therefore the sunniest.
Here are the average daily sunshine hours at the airport.
La Palma - Sunshine

Caldera de Taburiente

La Palma is a volcanic island; the southern part of the island is covered by a ridge of volcanic craters, among them Cumbre Vieja, an active volcano, 1,949 metres (6,394 feet) high, while the central part is occupied by the large Caldera de Taburiente, protected in a national park. On the edge of the caldera is the highest point of the island, Roque de los Muchachos, 2,423 metres (7,949 feet) above sea level, which being above the altitude where the trade winds blow, is generally above the clouds, and this is why here an astronomical observatory was built, the Gran Telescopio Canarias; from the top you can see, scattered in the ocean, other islands of the Canaries (Tenerife, La Gomera and El Hierro). At this altitude, winter is cold, so much so that highs hover around 7/8 °C (45/46 °F), and lows are near the freezing point; sometimes snow can fall, even abundant; in summer the temperatures are mild or pleasantly warm during the day (but with a very strong sun, which requires adequate protection, like sunglasses and hat), and cool at night.
Here are the average temperatures.
Roque de los M. - Average temperatures
Min (°C)112359131410742
Max (°C)78911141823221814118
Min (°F)343436374148555750453936
Max (°F)454648525764737264575246

Roque de los Muchachos, observatory and view

The sea in La Palma is quite cold in winter, though not prohibitively, and becomes warm enough for swimming from August to October. The island is located at a low latitude, almost at the Tropic, but on this side of the Atlantic Ocean a cold current runs, however, in this western part of the Canary Islands, the sea is slightly warmer than in the east, where the bulk of the cold current flows. The sea temperature goes from 19 °C (66 °F) in the period from February to April, to 24 °C (75 °F) in September.
Here are the average sea temperatures.
La Palma - Sea temperature
Temp (°C)201919192021222324232221
Temp (°F)686666666870727375737270

When to go

For swimming and sun bathing, the best period to visit La Palma goes from May to mid-October. In the first part (May-June), the air temperature is a bit lower and the sea is a bit colder, but the days are slightly longer. In the Canaries, in summer the days are shorter than in Europe (while in winter they are longer), but because of the time zone adopted, the sun sets late enough anyway.
To visit cities and for excursions in the interior, you can choose April, May and the first half of October.
In winter you will appreciate the mild temperatures and you can often sunbathe, although we can not exclude some days of bad weather. If you want you can combine a hike in the mountains, in search of the snow, with an afternoon on the beach.

What to pack in the suitcase

In winter: light clothes for the day, sweater and jacket for the evening, possibly a raincoat or umbrella. To climb mountains, down jacket, hat, gloves, hiking shoes.
In summer: summer clothes, but also a scarf for the wind, a light sweatshirt, a light jacket for the evening and for windy afternoons; comfortable shoes for hiking. For mountain climbing, hiking shoes, sweatshirt and jacket for the highest elevations.