Whilst not in Izumo at all, this modern ryokan in Tamatsukuri Onsen, about 9km southwest of downtown Matsue, has a minimalist but traditional aesthetic along the (clean) lines of less is more. Each room has a private, onsen-fed indoor/outdoor bath, and the service and dining will leave you feeling elevated. One for those who like the finer things in life.
KAI Izumo
Western Honshū