Gradually, free wi-fi is becoming available in more and more places but it’s still not as common as in many other countries. Often, you don’t know until you are inside the shop/cafe/restaurant and see the signs around announcing free wi-fi.
But it’s available at almost all 7-Eleven convenience stores. You can easily login/sign-up on the spot at the store.
7-Eleven is the largest convenience store chain in Japan and their stores are extremely common in all the major cities and towns… and can be easily spotted from a distance.
They also almost always have an ATM that you can withdraw cash from.
Japan Tourist Tips 