There is one maniac museum in Shibuya word, The Japanese Sword Museum (日本刀博物館). Katana (Japanese swords) are displayed all over in the museum. It has a collection of 120 pieces of swords and sword fittings including National Treasure and important Cultural Property.
The fee is 525 yen for an adult and you can get brochure in English. The title of brochure is “Manual of How to Handle and Take Care of Swords”. I found it is quite interesting even you don’t have any Katana. For instance, “Whether drawing out a Tachi or Katana, one must hold the cutting edge up and grasp the scabbard from underneath in the left hand in a forward holding position. Then, hold the hilt from above with the right hand” quotation from the brochure.
I admit the Katana are shinny and beautiful. There are even art. However, I felt it was OK because only Katana are displayed (there is an old Japanese armor displayed though) and maybe girls are less interested in this stuff. If you are Katana mania, this is must-visit place for sure.