Planing to go to Japan .?

This is not exactly apartment. But it's cheap and you can stay there for 1 month.

http://www.sakura-house.com/index.htm

In Japan foreigners cannot simply rent an apartment, and it is also extremely expensive.
In order rent an apartment the landlord will require you to have a job, pay one month rent in addition to one month rent worth for damage deposit plus 1 ~ 2 months rent worth for non-refundable key money.
As well, apartments are very small in Japan, and a 2 bedroom will go for over 130,000 yen per month in Tokyo depending on location.
Check out http://www.TokyoApartments.com
You'd be better off to stay in several youth hostels as you will likely want to do a lot of traveling, and you wouldn't want to leave all of your stuff in Tokyo for example, when you are traveling to Hiroshima, for example.
There is a ryokan in Asakusa in Tokyo which is actually cheaper than the Sakura Hotel in Jinboucho in Tokyo.
The cheapest form of overnight stay is a stay in a temple; the drawback is that you have to get up as early as the monks do, which could be 4am.

There should be many of these service apartments and apartment hotels in Japan for foreigners.

You might want to look here: http://gojapan.about.com/od/apartmentguesthouse/Apartment_Guest_House.htm

Landlords in Japan don't rent that way.You have to pay two or three months rent in advance, plus "key money".Key money is more or less of a bribe to the landlord to allow you to rent the place.This can be another month or two in rent money,but you'll never see it again.Also bear in mind many Japanese landlords won't rent to a non-Japanese.You will need an agent to help you.
Whatever you do,it's not going to be cheap.

This company I've know of for long time:

http://www.live-jpn.com/en/

Their background is strong since they've dealt with real estate business in tokyo for over 30 yrs, plus they have english speaker to assist you.

Your idea to go with an apartment is wise. Hotels really add up.

However, Japan has two basically unique problems that you won't find in other countries, when dealing with apartments: many landlords apparently don't want to rent to foreigners, and you are expected to pay out huge sums of money in security deposits and gift money to show your gratitude to the landlord. If you don't want to do these things, then I'd recommend you go with a gaijin house.

A gaijin house is an apartment building run for foreigners -- they are used to foreigners and do not collect things like key money that make regular Japanese apartments so expensive. They are cheaper in the short run, but more expensive in the long run. So if you were going to be in Japan for several years, perhaps it would be worth it to search for a regular apartment in a regular building, but since you're only going to be in Japan for one month, a gaijin house sounds like a better idea, at least to me.

Here is a chain of gaijin houses that has been recommended to me:
http://www.sakura-house.com/