1. Visit a shaved ice place called himitsudo. It has a really unique vibe and is completely off the beaten path (basically no signs in English on how to get there). One of my favorite experiences in Tokyo. http://bit.ly/1aSH3c2
    Suggested by @tudor
  2. Immersive digitally-controlled art installation of 2,300 flowers
    Only until May 1st http://bit.ly/1JJH8Lp
    Suggested by @maria
  3. Totoro Museum
    Not technically unusual... It might be too late to get tickets, but worth a try.
    Suggested by @maria
  4. Yomiuri Giants game
    Suggested by @lucas
  5. Wisteria tunnels
    It's quite a trip. This blog has good pictures http://bit.ly/1FSIDFu
    Suggested by @maria
  6. Tsukiji Fish Market
    go in the morning. get breakfast sushi. don't go to a place with a line. ask one of the knife stalls (Aritsugu or Miyakoya) where to go. buy a knife.
    Suggested by @lucas
  7. KAGAYA Bar in Shinabshi!!!
    This is a secret tiny basement bar in Shinbashi. It's hard to find (use google), down a small flight of stairs below a street level shop. The bar has 5 small tables and the owner/barman is Japanese man who does really dirty sketch comedy in broken English while he serves you drinks and makes fun of you while everyone else in the bar laughs. It's wonderfully weird and hard to describe(and I wouldn't want to give it away). If you love dick jokes, then this is the place for you...
    Suggested by @duro
  8. Tokyo DisneySea
    This is the second park at Tokyo Disneyland and it's honestly the most amazingly crafted theme park in the world and it's a pretty wacky culture clash experience too.
    Suggested by @lucas
  9. Cavern Club in Roppongi
    Beatles impersonators. The ultimate.
    Suggested by @laurimontclair
  10. Akihabara for some games. Play the claw game (UFO catcher ) to win a gloomy bear!http://bit.ly/1aVzUYm
    Suggested by @nickloris
  11. Candy Showtime Omotesando
    Not uniquely Japanese, but pretty amazing store where you can watch them make candy by hand w/ tiny messages inside. Fun.
    Suggested by @hollisbrown