I found the place where Chris trains/lives!
It’s at Palladium de Champéry in Valais, Switzerland!
The Champéry Palladium is a multifunctional complex that houses a restaurant, a hotel, a multi-purpose gymnasium with a stage and 3 fully-equipped conference rooms, tennis courts, pools, an ice rink, climbing wall, fitness room etc. It is also home to the National Ice Sports Centre.
Anyway the image below is a screencap from the episode and the images after are pictures of the actual place.
Stéphane Lambiel’s ‘Skating School of Switzerland’ is also based there by the way!