Beniyu looks like great choice. Seems minimalist and maybe a bit more westernized than your traditional Ryokan (IE: Gora Kadan or Shiraume). Also the food looks amazing on Instagram.

I've been doing a lot of research on super high-end properties within a short (1-2 hour train ride) of Tokyo, I've found a brand new hotel no one has mentioned.

Hiramatsu Atami - Is a luxury Auberge / Resort. Looks like it just opened late last year. The Japanese villas have both indoor and outdoor baths facing the ocean.