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I was looking for an inn near Kirishima Shrine, but it was already fully booked and I could not stay there, so I stayed at the Kirishima Folk Craft Museum which was available near Kirishima Onsen and very cheap at 3980 yen per night. It is a good hotel which is a little far from the hot spring town and very calm.
They exhibit antiques collected by the former chairman as a hobby, and you can see antiques from the Edo and Meiji periods.
The service was very friendly and the hot spring was very good, so I recommend this inn.

霧島神宮のそばの宿を探していたのですが、既に予約がいっぱいで泊まれなかったので、霧島温泉近くの空いていたとても安い一泊3980円の霧島民芸館に泊まりました。温泉街から少し離れており非常に落ち着いた良い宿です。
先代の会長が趣味で集めた骨董品を展示していて江戸時代や明治時代の骨董品を見ることができます。
接客もとてもフレンドリーで、温泉も大変良い、オススメの宿です。