JR is now offering free wi-fi for the passengers of the new Tohoku Shinkansen. We thank JR for its kindness as it is still not easy to find places with open wi-fi networks in Japan. However lately it seems the situation is improving a bit in preparation for the 2020 Olympics.
In addition to the free wi-fi in some train lines, stations and airports, you can also get wi-fi in 7-Eleven shops, Dennys restaurants and Starbucks. You will have to register in the service the first time you go online but once you do it you can seamlessly connect at any Starbucks/7-Eleven/Dennys.