Mobile Internet
Public WiFi
I’ve used to travel only with public hotspots, but they are not always available and don’t make the trip very comfortable.
SIM Card
You can get some data SIM cards easily at BIC Camera, Yodobashi Camera and usually they should also be at the airport. That’s what I used most of the time I travelled and this worked very well for me.
Pocket WiFi Router
I don’t have experience with them myself, but you also have the option to rent a Pocket WiFi Router. Since I can’t give myself info on that, I’ll have to link to this article.