Japanese people tend to choose the top three in every field. In most cases, someone or a group with influential authority selected the top three, and the selections were settled.
These selections are used by the chosen places to promote tourism. They always refer to the selection in their guiding explanations.
Wikipedia 日本三大一覧 https://ja.wikipedia.org/wiki/日本三大一覧#観光地理学
Mark <*> shows the three is not perfectly set.
Three Sacred Mountains: Mt. Fuji, Mt. Hakusan, Mt. Tateyama
Three Sacred Places: Mt. Osore, Mt. Hiei, Mt. Koya
Three Shinto Shrines*: Ise (Mie), Iwashimzu (Kyoto), <Kamo (Kyoto) or Kasuga (Nara)>
Three Sumiyoshi Shrines: Sumiyoshi (Osaka), Sumiyoshi (Shimonoseki), Sumiyoshi (Fukuoka)
Three Hachiman Shrines: Usa Hachiman (Usa), Iwashimizu Hachiman (Yawata, Kyoto), Hakozaki (Fukuoka)
Three Inari Shrines*: Fushimi Inari (Kyoto), Toyokawa Inari (Toyokawa, Aichi), <Yutoku Inari (Kashima, Saga) or Kasama Inari (Kasama, Ibaraki)>
Three Tenjin Shrines*: Dazaifu (Dazaifu), Kitano(Kyoto), Hofu (Hofu, Yamaguchi)
Three Big Buddha Statues*: Nara, Kamakura, <Takaoka or Gifu>
Three Five-Storied Pagodas*: Horyu Temple (Nara), Ruriko Temple (Yamaguchi),<Daigo Temple (Kyoto) or Mt. Haguro (Yamagata)>
Three Front Temple Gates*: Aso Shrine (Aso), Kashima Shrine (Kashima), Hakozaki (Fukuoka) —Kuon Temple (Yamanashi), Nanzen Temple (Kyoto), Chionin Temple (Kyoto)
Three Temple Bells: Chionin Temple (Kyoto), Hoko Temple (Kyoto), Todai Temple (Nara)
Three Temple Bells with Beautiful Sound: Hoko Temple (Kyoto), Byodoin Temple (Uji), Ennjo Temple (Otsu)
Three Sand Dunes*: Tottori Dune (Tottori) Fukiage Beach(Kagoshima), <Nanendai Dune (Shizuoka) or Syonai Dune (Yamagata)>
Three Pine Grove Beaches*: Miho-no-Matsubara (Sizuoka), Niji-no-Matsubara (Karatsu) <Amanohashdate (Kyoto) or Kehi-no-Matsubara (Fukui)
Three Karst Plateaus: Akiyoshidai (Yamaguchi), Hiraodai (Fukuoka), Shikoku Karst (Ehime/Kochi)
Three Limestone Caves: Ryusendo (Iwate) , Syuhodo (Yamaguchi), Ryugado (Kochi)
Three Rapid Rivers: Fuji River, Kuma River, Mogami River
Three Clear Rivers: Shimanto River, Nagara River, Kakita River
Three Waterfalls: Nachinotaki (Wakayama), Kegononotaki (Nikko), Fukurodanotaki (Ibaraki)
Three Old Onsens: Arima, Nanki Shirahama, Dogo
Three Onsens: Atami, Nanki Shirahama, Beppu
Three Onsens for the Beaty: Kawanaka (Gunma), Ryujin (Wakayama), Yunokawa (Shimane)
Three Onsens for the Skins: Ureshino (Saga), Hinokami (Shimane), Kitsuregawa (Tochigi)
Three Night Views: Mt. Hakodate (Hakodate), Mt. Maya (Kobe), Mt. Inasa (Nagasaki)
New Three Night Views: Mt. Sarakura (Kitakyushu), Fruits Park (Yamanashi), Mt. Wakakusa(Nara)
Three Extraordinary Sights: Yabakei (Nakatsu), Kankakei (Shodo Island), Mt. Myogi (Gunma)
Three Good Views: Matsushima (Miyagki), Amanohashidate (Kyoto), Miyajima (Hiroshima)
Three Japanese Gardens: Kenroku Garden (Kanazawa), Koraku Garden (Okayama), Kairaku Garden (Ibaraki)
Three Secluded Regions: Shirakawago (Gifu), Iyayama Village (Tokushima), Shiiba (Miyazaki)
Three Momiji Viewing Places: Nikko (Nikko), Mt. Arashiyama (Kyoto), Yabakei (Nakatsu)
Three Festivals: Gion (Kyoto), Tenjin (Osaka), Kanda (Tokyo)
Three Bizzare Bridges*: Kintai Bridge (Iwakuni), Saru Bridge (Yamanashi), < Aimoto Bridge (Toyama) or Kisonokakehashi (Nagano) or Kadura Bridge (Tokushima)>
Three Best Castles: Himeji Castle, Osaka Castle, Nagoya Castle
Three Delicacies: Karasumi (Nagasaki), Konowata (Aichi), Sea-Urchin (Fukui)
New Three Delicacies: Kusaya (Nijima Island), Funa Sushi (Shiga), Kurotukuri (Toyama)
Three Soba Noodles: Wanko (Iwate), Izumo (Shimane), Togakushi (Nagano)
Three Udon Noodles*: Sanuki (Kagawa), Inaniwa (Akita), <Kishimen (Nagoya) or Mizusawa (Gunma)>—Goto (Nagasaki), Inaniwa, <Himi (Toyama) or Mizusawa>
Three Green Tea: Uji (Kyoto), Shizuoka (Shizuoka), Sayama (Saitama)
Three Beautiful Wild Woods: Aomori Hiba (Hiba cypress), Akita Sugi (ceder) Kiso Hinoki (Hinoki cypress)
Three Beautiful Planted Woods: Tenryu (Shizuoka), Yoshino (Nara), Owase (Mie)
Three Cherry Blossoms: Miharutaki (Fukushima), Jindai (Yamanashi), Usuzumi (Gifu)
Three Sake Breweries: Nada (Kobe), Fushimi (Kyoto), Saijo (Hiroshima)Three Good Views on Railroads: Niinai Station on Nemura Line, Obasute Station on Shinonoi Line, Yatake Station on Hisatsu Line