[Nyororin]

Forget Sakura House or any of those gaijin communal places - in the end you`ll find yourself with lots of friends... But probably very few who speak Japanese which seems it would defeat the entire purpose of your stay. Plus, they`re expensive for what they are (very much so).

Look into Leopalace. You can find them ANYWHERE in Japan - not just major foreigner areas - and they are very cheap. You can usually rent a private apartment that is quite nice and clean - and that is furnished and includes all utilities and unlimited internet access - for around 50,000/month. You can stay in one for the entire length of your tourist visa but will just need to pay ahead in cash. (Something that shouldn`t be a problem if you`re not planning to work anyway)
They also often have good deals to change locations midway to another apartment of the same price rank in another city. You could move to a few different areas during your time.