The Musée Basque, technically in Bayonne (10 minutes from Biarritz), is the best museum in the region for understanding the Basque culture that underlies and permeates the resort-town surface of Biarritz. The collection covers Basque folk art, traditional rural life, the pelota sport, and the maritime history of the Basque coast, including the extraordinary 16th and 17th century whaling expeditions to Labrador and Newfoundland that made Basque sailors the dominant force in the North Atlantic.
The building itself is a fine 16th-century manor house in Bayonne's old town. The displays are well organised and most have English-language texts. If you are spending more than a day in the area and want to understand why the villages look the way they do, why everyone is playing pelota, and why the food tastes the way it does, this museum explains it. Combine with a walk through Bayonne's old town and the Gothic cathedral.