You can spend some time walking around the town. I was unlucky and had a very rainy partial day there, and I was not impressed. However, I did enjoy the Musee Asiatica, a private museum with a nice collection of Asian decorative art.
I much preferred Bayonne, but I haven't checked transportation schedules to see whether spending the night there, rather than in Biarritz, would be practical in your situation. Bayonne has a good Musee Basque and a chocolate museum that had a generous tasting room as of 2019. The historic center is rather large, extending over both sides of the River Nive.
I assume some others here have been happier with Biarritz than I was and can give you some good suggestions.
I believe Rick covers the French Basque Country in his guide to Spain, which I'd think would be useful to you at other points of your journey.