I have found that one of the best ways to immerse yourself in a foreign culture is to attend a local sporting event. My husband & I happened to be in Tokyo during the annual sumo wrestling tournament. So we bought the cheapest tickets that were available on the last day of the tournament and spent an entire afternoon watching each division of wrestlers up to the grand finale.
Between matches we toured the arena, admired the beautiful hand-crafted silk robes of the elite wrestlers, and ate the traditional sumo food—a big bowl of hearty soup called chanko. We only saw a handful of non-Japanese people and most attendees didn't speak English. But that's exactly what we had hoped for, to be a part of a unique cultural event that wasn't being performed for the sake of tourists. My favorite part was the ring entering ceremony (pictured here) performed by the makuuchi division. Watching the final bout was pretty exciting, too!
If you aren't able to catch one of the three annual 15-daylong grand tournaments, ask your concierge if they know of a 'beya' where you can sit in on a training session. Training is early, around 6am, and you'll need someone who speaks Japanese to arrange it for you—well worth the early wake-up call though!