Map from Google - Azores

The climate of the Azores Islands is very mild, being subtropical oceanic, cool or mild for many months and pleasantly warm in summer: therefore they are not a tropical paradise. The Azores archipelago, which is a Portuguese autonomous region, is located in the Atlantic Ocean at the same latitude of the Mediterranean Sea, but the influence of the ocean makes the climate even milder, especially in summer, which is cooler.
In fact, the winter temperatures range from 11/12 °C (52/53 °F) at night to 17/18 °C (63/64 °F) during the day, while in summer, they range from 17/18 °C (63/64 °F) at night to 24/26 °C (75/79 °F) during the day. From month to month the temperatures vary slowly, so highs exceed 20 °C (68 °F) only from June to October. The highest recorded temperatures in the Azores are not impressive: they almost never reach 30 °C (86 °F) even in summer. On the other hand, temperatures rarely drop below 7/8 °C (45/46 °F) in winter.
Here are the average temperatures of Ponta Delgada, in the island of São Miguel.
Average temperatures - Ponta Delgada
Ponta DelgadaJanFebMarAprMayJunJulAugSepOctNovDec
Ponta DelgadaJFMAMJJASOND
Min (°C)121112121315171818161413
Max (°C)171717182022242625222018
Min (°F)545254545559636464615755
Max (°F)636363646872757977726864

The Azores gave their name to the famous anticyclone (high pressure area) that brings fine weather on Western Europe and the Mediterranean (Azores High), however in these islands the weather is not always sunny. In fact, in autumn and winter, the rains are frequent, and in the north-western islands they are also abundant.
Due to the abundance of rainfall, the landscape is green and blooming; flowers bloom mainly in spring and paint the landscape, as evidenced by the name of the westernmost island, the very rainy Flores ("flowers").
Here is the average precipitation of Santa Cruz, in the island of Flores.
Average precipitation - Santa Cruz
Santa CruzJanFebMarAprMayJunJulAugSepOctNovDecYear
Santa CruzJFMAMJJASONDY
Prec. (mm)180160165110857060801101201401601440
Prec.(in)7.16.36.54.33.32.82.43.14.34.75.56.356.7
Days161415111086811131315140

The rainfall doesn't reach 800 millimetres (30 inches) per year in the island of Santa Maria (the southeasternmost island), it's just above this value in Santa Barbara, while it exceeds 1,000 mm (40 in) in the other islands. In the summer months, from June to August, the rains are a bit more rare and less abundant, but they still occur for 5/7 days per month on average.
Here is the average rainfall of the aforementioned Ponta Delgada, in the southeastern island of São Miguel.
Average precipitation - Ponta Delgada
Ponta DelgadaJanFebMarAprMayJunJulAugSepOctNovDecYear
Ponta DelgadaJFMAMJJASONDY
Prec. (mm)120100105656040253080105120100950
Prec.(in)4.73.94.12.62.41.611.23.14.14.73.937.4
Days1413131097569121314125

The amount of sunshine in the Azores is not abundant, especially in the period from October to April, when the skies are often cloudy. Besides, there's no shortage of wind storms in the period from November to March.

Some of the islands are covered by hills or mountains. The highest peak is Mount Pico, a volcano of 2,351 metres (7,713 feet), in the island of the same name. The slopes of the mountain are often covered by clouds, and are very rainy, while the summit can be covered with snow in winter and spring.

Azores

For swimming, the ocean is a bit cool in summer, but still acceptable, at least for those who are not sensitive to cold: the water temperature is 22 °C (72 °F) in July, and 23 °C (73 °F) in August and September.
Sea temperature - Ponta Delgada
Ponta DelgadaJanFebMarAprMayJunJulAugSepOctNovDec
Ponta DelgadaJFMAMJJASOND
Sea (°C)171616161719222323211918
Sea (°F)636161616366727373706664

When to go

The best time to visit the Azores is summer, from July to August, being the warmest and sunniest; having an oceanic climate, the Azores experience a delay in the sea warming, which affects the air temperature as well, so that September is warmer than June, and the temperature is still the same as in the summer, even though the rains become a bit more frequent. In July and August, the temperatures are pleasant, the sunshine amount acceptable, the rains not very frequent, while June is a bit cooler and more cloudy.

What to pack

In winter: spring/autumn clothes, sweater, jacket, raincoat.
In summer: light clothing, but also a sweatshirt or sweater, light scarf for the wind, light jacket, raincoat or umbrella.