Takamiya is an atmospheric, upmarket ryokan that has been in business for nearly three centuries. There are several beautiful indoor and outdoor baths, while the spacious rooms have tatami sitting areas and fluffy wa-beddo (thick futons on platforms). Meals are traditional kaiseki ryōri (formal, multiple-course banquets) featuring top-grade local beef. Staff go above and beyond to offer exceptional hospitality.
It's not cheap, but it's a true destination and worth the splurge, especially with a loved one.