From today’s Nikkei. I would like to visit every one of these places.
Among the closer options, perhaps Yagyu-no-Sho or Keiunkan.

Western Japan
Yufuin Tamanoyu from ¥34,800 0977-84-2158
Nishimuraya Honkan (Kinosaki Onsen, Hyogo Prefecture) from ¥29,550 0796-32-2211
Kagaya (Wakura Onsen, Ishikawa Prefecture) from ¥28,500
Monjusou Shourotei (Amanohashidate Onsen, Kyoto Prefecture) from ¥26,400
Yufuin Onsen Kamenoi Besso from ¥34,800

Eastern Japan
Akan Tsuruga Besso Hinanoza from ¥28,500
 All 25 rooms have open-air baths
Yagyu-no-Sho (Shuzenji Onsen, Shizuoka Prefecture) from ¥45,000
 Of its 16 rooms, 5 have open-air baths. It is also renowned for its distinctive kaiseki cuisine
Tsutsujitei (Kusatsu Onsen, Gunma Prefecture) from ¥33,750
 Of its 10 rooms, 4 have semi-open-air baths
Myojinkan (Tobira Onsen, Nagano Prefecture) from ¥22,150
 Of its 45 rooms, 15 have open-air or semi-open-air baths
Koshu Nishiyama Onsen Keiunkan (Nishiyama Onsen, Yamanashi Prefecture) 0556-48-2111
 Free-flowing hot spring water is even used in the indoor baths and washbasins in the guest rooms