Where and what price to rent a motorbike in Japan to travel around independently. What are normal prices? Based on the price I am thinking either a 5 to 20 day period.
I have no special expectation of which bike to rent. Just something possible to travel a couple of hundred km. A plus might be to go through a light terrain (not necessary).
I will arrive at Osaka but I plan to travel all around Japan, so the question is rather in general.
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). E. g. Kawasaki Ninja 400cc for ¥ 14,000 for the 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 (half for other days) for the same kind of motorbike. They don't offer interesting discounts for longer rental period however. They have an office in almost every big city. Read more about insurance below.
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 insurance conditions. Even though Japan is a safe place in terms of criminality and drive safety you are still at a risk of high costs in case of problems.
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.
Thanks to uncovery for providing a search term "レンタルバイク" 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, although they have experiences only with car rentals.
However I finally rented a car there because of a bad weather (check weather for typhoons). It is also much cheaper, easier and with better conditions (starting below ¥ 4,000) although not such a fun..
This is not easily, generally answerable however. Prices in Japan vary heavily depending where you are. Renting a car in Okinawa, Osaka and downtown Tokyo will have quite different prices, same goes for motorbikes.
On top of that, as you probably know, bikes vary in spec massively. Since you do not indicate if you want to rent a 50cc or a custom-built Harley, a price will be even harder to determine.
I also want to point out that unless you speak Japanese well enough to discuss contract terms, you might have issues with some companies to get a contract signed. On top of that, some smaller Japanese companies might not rent to foreigners, no matter how well you speak Japanese. They will want to have a Japanese phone number and/or address.
If you know someone in Japan who can assist you (maybe even your hotel in Osaka can do that) to find a company that will give you a bike, this will of course be very helpful.
So planning will be crucial in this. There are several companies renting out bikes obviously. If you want to Google yourself, the term is "rentalbike", in Japanese "レンタルバイク" and Osaka is written "大阪"
Googling that, the first company on the results for example rents out a variety from 50cc to 1200cc, starting with 4'000 Yen a week for the smallest and topping out at 25'000 Yen for a week. I guess you will have to pick your preferred model.
