That's actually really tough in this global age. I live in Japan so things like tea ceremony and Shinto practice come to mind, but there are Shinto shrines and practitioners in many places and people do and teach tea ceremony in other places now. Many would call it the home of sushi and, at least for the common types today, it's probably true (though certain methods that led to sushi are thought to come from Viet Nam in the past).

Tanuki exist in other parts of Asia. I assume onsen (hot sprint) monkeys do as well. Maybe something with Wasabi, but I doubt it. I'm not sure, really.

Edit: thought of one: seeing the Iriomote cat in its natural habitat (although that's really hard since they were nearly hunted to extinction for their pelts at one point). Speaking of Okinawan islands, you can also see Taiwan on a good day from the westernmost point of Yonaguni. That was neat. I took a picture with my phone at the time and it's really hard to see anything, but I could see land with my eyes.