Iwaso Ryokan
For traditional elegance, it's easy to like this venerable Japanese inn. It's the oldest and most famous lodging on the island, and everyone important has stayed here. The rooms in the wheelchair-accessible newer wing are nice enough, but the older rooms have more character. Two quaint cottages on the grounds have suites decorated with antiques. Prices vary widely according to the size of your room, the view, and the kaiseki dinner you select, so be sure to get it all ironed out when you make reservations. Breakfast and dinner are usually included in the rates and can be made Western-style. Nonguests can also enjoy the food.