Things to do in or near Biarritz

Not really an answer here to your question. If you are asking about any significant history site in Biarritz, maybe tracking down this one is a possibility: Napoleon III met with Bismarck in Biarritz, prior to 1870, obviously.

I would assume that site would have a plaque or information of that site can be provided by the Tourist Office.

When I was in Rouen this past trip, it was the young lady in the Tourist Office who enthusiastically provided me with information on getting to the Napoleon statue....bravo !

On sites pertaining to WW1, especially, I can help you much more if your itinerary includes other areas of France.

I think Rick covers the French Basque Country in his guide to Spain.

Bayonne has an attractive historic district and several good museums. The chocolate museum had a generous tasting room as of 2019. Public transportation available from Biarritz. The chocolate museum is a bit of a walk from the nearest public-bus stop.

St-Jean-de-Luz is picturesque. Public transportation available Biarritz.

Biarritz itself has a privately-run museum of Asian art that I enjoyed. It's mostly decorative art, and I think mostly from South Asia. I was otherwise not thrilled with Biarritz, but I hit a very rainy day, which never helps.

Rick mentions some mountain villages on the French side of the border. They'd be easier with a car. If I had a car, I'd make a point of getting into the mountains.

You can cross into Spain without a car. Either Hondarribia or San Sebastian would be a practical day trip, I guess, if you don't mind a good bit of time sitting on a local train. Bilbao would really take too long.