Due to me searching for somewhat the same (japanese classes + 3 month apartment stay) I came across the following within a nice budget (or well, its not so expensive like the many other alternatives I came across
):
Japanese Language School - MLC Meguro Language Center (in Tokyo, Japan) 2.5 month beginner class for 118k yen.
As for housing in tokyo, sakura-house.com provides a great deal of guesthouses/apartments across Tokyo. Easy system focused on short-term staying foreigners (1 month - 1 year) and it aint too expensive.
And johnnyboydave, you seems to be missing some information; after 5 years of staying in Japan you dont become a permanent resident but you will just have completed
_one_ of the qualifications of becoming a permanent resident.
Read this story, it may make things a little more clear for you:
click.