Personal experience: there are multiple websites which offer renting of portable wifi router. Most of them offer an easy pickup at the major airports (for example this one). At the end of your holiday you just give it back using a mail box with the provided envelop.
But the problem I experienced is that it's easy to manage if you are max 2 people. But more than 2 it gets difficult since in crowded places people can start to walk away, maybe get lost (it happened twice to me) and so they are out of connection. The problem could be even worse if, like in my case, your local SIM will be completely offline in Japan.
So my advice is to buy a local SIM, which has a reasonable traffic limit at a much lower price than the router. They are sold everywhere, also at the airport. Of course each person has to buy one, but I think it's much easier to handle. And in an expensive trip such as one in Japan, I don't think 50 euros (or dollars) more for a SIM card will change your life.