Yes, it is quite safe to drink tap water in Japan. Tokyo Waterworks writes on their homepage that the tap water is completely safe to drink and has a soft taste. Technically the water is soft and is that gives a strange taste for me who is used to hard water. If you don’t like the taste or need water when outside, then every convenience store sells a big water bottle for ~100 yen (7-10 NOK).

My journey to the Land of the Rising Sun started with me arriving at my local airport around two hours before I would sit in a big, flying metal tube for many hours. I had (or technically, my wife) packed two full suitcases and two pieces of carry-on. Everything I would need to support my self for the initial part of my adventure was in those bags. Clothes, shoes, pillows, coat hangers, and other useful stuff all packed inside those bags with only a few grams of margin before reaching the airline limits.