Map from Google - Basque_Country

In the Basque Country (Euskadi in Basque, or País Vasco in Spanish), an autonomous community in northern Spain, the climate is cool and damp on the coast, because of the influence of the Atlantic ocean, while in inland areas it becomes colder with increasing altitude, and a little more continental and more arid in the south.
Along the coast the wind blows frequently, in fact there are beaches frequented by surfers.
Winter on the coast is quite mild, but sometimes cold air masses from the northeast can bring cold periods, in which it can also snow, and frosts may occur, typically light. This happens more easily in the eastern part of the coast (see San Sebastián), than in the west (see Bilbao).
The rains are quite abundant in the northern part of the Basque Country, where they typically exceed 1,000 millimetres per year; in the central part instead they drop below 800 mm, and in the far south, where the landscape becomes much more arid, even below 500 mm. Summer is everywhere the least rainy season.
In the interior we find hills and mountains: the Basque Mountains, which are part of the Cantabrian Mountains, separate the cool and damp part of Spain from the arid plateau (Meseta); the highest point is the massif of Aizkorri, which reaches 1,551 metres.
The wind that comes down from the mountains may cause rapid increases in temperature, due to the föhn effect, so that along the coast the temperature may exceed 20 °C in winter, 30 °C in autumn and spring, and 35 °C in summer, when, however, this wind is rare.
The coast, overlooking the Bay of Biscay (or Vizcaya) is indented, and characterized by cliffs that plunge into the sea and by caves, but also by beaches.
In the west, a short distance from the coast we find Bilbao: here the average temperature of January is 9.5 °C, that of August is 21 °C; in a year almost 1,200 mm of rain fall, with a maximum in November (145 mm), and a minimum in July (50 mm).
In the eastern part of the coast we find San Sebastián. Here the average temperature of January is 8.5 °C, that of August is 19.5. Although the winter temperatures are typically mild, this eastern part of the coast is, as mentioned, more exposed to cold air outbreaks, and consequently to snow and frost. The temperature dropped to -9 °C in January 1985, and to -5 °C in February 2012. In summer, although generally the temperatures are mild, there may be short heat waves. In August 2003 the temperatures touched 38.6 °C.
Here are the average temperatures of the Igueldo station.
Average temperatures - San Sebastián
San SebastiánJanFebMarAprMayJunJulAugSepOctNovDec
San SebastiánJFMAMJJASOND
Min (°C)667811141617151297
Max (°C)111213151820222321191412

The rainfall in San Sebastián amounts to 1,500 mm per year: we are in the wettest area of the coast (in the Hondarribia airport, slightly further to the east and at the border with France, it gets to 1,650 mm). Summer is the least rainy season, but it still rains 10/11 days per month, and the amount does not drop below 85 mm in July.
Here is the average precipitation.
Average precipitation - San Sebastián
San SebastiánJanFebMarAprMayJunJulAugSepOctNovDecYear
San SebastiánJFMAMJJASONDY
Prec. (mm)14011011514012090851151101601701501510
Days131212141211101110121313142

La Zurriola, beach

In the central part of the Basque Country, in the area called Llanada Alavesa, the weather gets colder in winter, and a bit warmer on summer days.
In Vitoria-Gasteiz, the capital, located at 500 metres above sea level, winter gets cold enough, but above all the city is exposed to invasions of cold air, which can produce snow and frost: on average, 11 days of snow per year occur, from November to April. In summer, average temperatures are similar to those of the coast, although during the day it can get hot with a higher frequency, while nights are definitely cool.
Here are the average temperatures.
Average temperatures - Vitoria-Gasteiz
Vitoria-GasteizJanFebMarAprMayJunJulAugSepOctNovDec
Vitoria-GasteizJFMAMJJASOND
Min (°C)1134710121310842
Max (°C)9101415192326262318129

Precipitation amounts to 750 mm per year, the rainiest month is November with 90 mm, the least rainy July, August and September with 40 mm.
Here is the average precipitation.
Average precipitation - Vitoria-Gasteiz
Vitoria-GasteizJanFebMarAprMayJunJulAugSepOctNovDecYear
Vitoria-GasteizJFMAMJJASONDY
Prec. (mm)756565737045404040709080750
Days10108119645691111100

Vitoria-Gasteiz in the snow

In the southern part of the Basque Country, in the Ebro Valley (the area called Rioja Alavesa, see Laguardia), the climate gets semi-continental features, similar to those of the Meseta: semi-arid (annual rainfall drops below 500 mm per year), with quite cold winters (the January average is around 6.5 degrees), and hot summers, when there may be some torrid days, while nights remain pretty cool. It is an area renowned for its wine.
Here are the average temperatures of Logroño, located in the same area, though on the south bank of the Ebro River, and thus in the La Rioja province.
Average temperatures - Logrono
LogronoJanFebMarAprMayJunJulAugSepOctNovDec
LogronoJFMAMJJASOND
Min (°C)22561013161613953
Max (°C)101216182227303026201410

In Logroño, just 435 mm of rain per year fall, with a maximum in April and May (50 mm) and a minimum in August (20 mm). Autumn and winter are not very rainy, because Atlantic currents arrive with difficulty in this area, due to the barrier formed by the aforementioned Basque Mountains.
Here is the average precipitation.
Average precipitation - Logrono
LogronoJanFebMarAprMayJunJulAugSepOctNovDecYear
LogronoJFMAMJJASONDY
Prec. (mm)302530505045302025404540435
Days66589644477771

Rioja Alavesa

The amount of sunshine in the Basque Country is never very good, at least in the northern and central part: in July and August there are 6/7 hours of sunshine per day in Bilbao and San Sebastián, and 7/8 in Vitoria; in the other seasons, and especially in late autumn and winter, it is even worse, and the sky is often cloudy. On the contrary, in the south, in the valley of the Ebro the summer is sunny.

For swimming, the sea in the Basque Country is very cool, if not a bit cold, even in summer, since its temperature peaks at 20/21 degrees from July to September, as you can see from the temperature of the sea at Bilbao.
Sea temperature - Bilbao
BilbaoJanFebMarAprMayJunJulAugSepOctNovDec
BilbaoJFMAMJJASOND
Sea (°C)131212131518202120181513

When to go

The best time to visit the Basque Country, at least the center-north, is the summer, from June to August or the first half of September, being the driest and sunniest. July and August are the warmest and least rainy months. Even in midsummer you must take into account some rain, and some nights a little cool on the coast, and a bit cold in the central inland areas.
In summer, in good weather you can take a break at the sea and sunbathe, with an air temperature often pleasant and a cool breeze from the ocean, although as I said the sea is a bit cold for swimming.
In the south, the Ebro valley, since in summer can be very hot, can be visited in spring and autumn, especially in May, and from mid-September to mid-October, although the rains are more frequent; in autumn, the landscape occupied by vast vineyards shows spectacular colours.