If Wimbledon has the All England Lawn Tennis and Croquet Club, Tokyo has the Tokyo Lawn Tennis Club. Both are more than 100 years old, both are rich in tradition, and both require players to dress up in white when using the club. One big difference would be the former hosts a yearly tournament known the world over.
I’m pretty sure membership is by invitation only and unless you are royalty or a member of the diplomatic corps, you are very unlikely to get an invitation.