The Iwasō, open since 1854, offers a grand ryokan experience amid exquisite gardens. There are three wings; a stay in a lovely 'Hanare' cottage will set you back the most. Not all rooms have private bathrooms, but you can soak in the onsen in the main building. It's especially stunning in autumn, when Momiji-dani (Maple Valley) explodes with colour.
It's about a 15-minute walk from the ferry port, or a pick-up can be arranged.