I don't think you understand distance. Japan is a country 25% larger than Italy. If you think you can go from Sicily to Rome to Naples and Venice in one week and get something out of that, then feel free to do the same thing in Japan.

There are plenty of cheap hotel options, you're just looking in the wrong place.
Have you tried using TripAdvisor? If you want to do Japan on the cheap there are plenty of business hotels that have tiny rooms but will only run you about 50 EUR a night. And yes, you will be unlikely to get Priority Club points, but at 50 EUR do you really care?

Lastly, we can't spell everything out for you, that's not our job. You should know this after 700+ posts on this forum.