After my return from Japan (visited north to south from Abashiri to Yakushima) I would choose as a good example of a motorbike rental http://www.eaglejp.co.jp/rental/ in Sapporo ([English translation][1]). E. g. Kawasaki Ninja 400cc for ¥ 14,000 for first day and half of the price for other days and lot of other models/prices. 

They have no problem to rent a bike to a foreigner with an international driving license. People at information office at Sapporo JR station can call them for you to check it as well as consult insurance conditions (see below).

The biggest motorbike rental network in Japan is http://www.rental819.com/english/ with ¥ 15,000 + ¥ 3,000 on [collission damage insurance][2] (half for other days).  It does not offer interesting discounts for longer rental period however. Read more about insurance below. It has an office in almost every big city. 

## Problematic Insurace ##
However I found a relatively unpleasant point of the bike rental an insurance (contrary to a car rental). Standard is you will pay a half of the price of the bike if it gets stolen with no option to pay for better conditions. Even though Japan is a safe place in terms of criminality and drive safety you are still at risk of high costs in case of problems. 

## Best place to rent##

The friendliest place to rent a motorbike seams to me Sapporo. It is easy to go outside a city (contrary to cities like Tokyo/Osaka/Kyoto) and there are lots of scenic roads around a shore or through mountains on Hokkaido. 

## How I found the info ##

Thanks to *uncovery* for providing a search term "[レンタルバイク][3]" which I used on each place to search in Google maps and translating with Google translator. (Results include also some bicycle rentals which you must ignore.) I consulted it also with tourist information office in some of the cities or Japanese people in hostels to get more information. They will try to help you as they can searching the web however they have experiences only with car rentals. 

However I finally rented a car there because of a bad weather ([check weather for typhoons][4]). It is also much cheaper, easier and with better conditions (starting below ¥ 4,000) although not such a fun.. 


  [1]: http://translate.google.com/translate?sl=auto&tl=en&js=n&prev=_t&hl=en&ie=UTF-8&u=http://www.eaglejp.co.jp/rental/
  [2]: http://www.rental819.com/english/rates_insurance.php
  [3]: https://www.google.cz/maps/preview#!q=%E3%83%AC%E3%83%B3%E3%82%BF%E3%83%AB%E3%83%90%E3%82%A4%E3%82%AF&data=!4m10!1m9!4m8!1m3!1d6670699!2d136.814655!3d38.9328219!3m2!1i1436!2i806!4f13.1
  [4]: https://play.google.com/store/apps/details?id=wni.WeathernewsTouch.jp