We loved our stay at Latour D'affaure's place. It is an older style apartment (but has a lift to help get your bags up the stairs). The apartment could be described as quintessentially french (it was older, unpolished wooden floors, no fuss, but splashes of colour, tidy, quite spacious, and comfortable).
It was honestly THE BEST LOCATION. There is a great market 2 streets up where we bought fresh produce every morning. Wherever you are in Biarritz, you are only a short walk from the apartment. It's really central. The beds were comfortable, and Latour was a wonderful host.
Beware that getting a taxi from the airport in Biarritz into town can be challenging (we waited for 1.5 hours at the airport). I would recommend pre-booking one if you can (which you will most likely need to do, if you take an evening flight).
Highly recommend the apartment and Biarritz.