I think more and more young Japanese people prefer a Western-style wedding nowadays; however, the Meiji Shrine in Tokyo probably remains the most famous and traditional place for Japanese Shinto wedding ceremonies. The nice thing is that almost every weekend you can observe bridal couples and with their families and guests as they walk across the shrine grounds to and from the actual ceremony. Not that Meiji Shrine itself isn't worth a visit, but combining it with a glimpse of this traditional Japanese custom is quite something.
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Find out more about Meiji Jingu Shrine.