I am looking into a visit to Japan after crossing the Trans-Siberian Railway. I was hoping to stay approx. two?

months in Japan in order to successfully employ my language skills and to enjoy the new environment. However, I have heard that one month is probably a more reasonable period of time to spend. I am not very interested in staying with a hosting family considering my independent nature. However, I am curious, how many U.S. dollars should I save up before planning such a trip? Are there houses for rent to foreigners on an extended stay? How does one go about getting a visa and where is a good place to stay? I would prefer a place out in the country, but I know that travel to the bigger cities will then be quite expensive. Thanks a bunch. :)