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Using Booking dot com you can find in the whole country and filter by "hostel" so you can get at once all the prices. Specifically for Japan here's the link sorted by price and filtered to show only the hostels. You have more than 1000 options to choose from 7 euros.
This is just an example and have in mind that Booking has not all hostels in Japan, but probably most of them.
Note that if you just want the list of cities with hostels, you can refer to the list that appears in the left sidebar once you filter by "hostel" (26 cities in the example).