Takamiya is an atmospheric, upmarket ryokan that has been in business for nearly three centuries. There are several beautiful baths here, both indoor and outdoor, made of stone or aromatic cedar. Meals are traditional kaiseki ryōri (formal, multiple-course banquets), with top-grade local beef as the headliner. The spacious rooms have tatami sitting areas and fluffy wa-beddo (thick futons on platforms).
It's not cheap, but it's a true destination and worth the splurge, especially with a loved one.