Living and Travelling in Japan

I have $10,000 and I will be in Japan in November. I was a bit curious as to, if people travel and such in Japan, how long people usually last till they burn through a lot of cash. Now I'm sure it differs, but I'm more into just living, train expenses and dormitories...etc

How much is the trains and different train companies roughly in osaka or tokyo?
How are the dormitories over there for foreigners? (short term stays..)

I have been looking into apartments and such, but I only wanted to live in Osaka and Tokyo for 3 months each before moving to a different city as before i settle and get a job somewhere, so as not to die of starvation (ha-ha).

I apologize if someone has already posted something like this, but some information is a bit vague from others. Thanks a lot.

Darkoa I assume that's $10,000 AU given that you are from Perth?(same hometown as me)

You can live comfortably with $10k for 6 months as long as your not a gadget guy who is tempted with things.
Cost of rent has been done a thousand times on this forum so rather I won't repeat what others say, just try the search :)

Short distance travel around the cities generally costs 200-300 yen but can greatly increase with distance. Not that much different from Perth actually.
There are companies that offer short term stay apartments. I believe a few have been mentioned on this forum as well as google 'Short term apartment Tokyo' does find several useful results.
The cost might impact your $10k however so make sure you look into all costs associated with the apartment. Some apartments charge you extra for certain things like kitchen tools (sounds stupid), internet etc..

If you are looking to settle in there after those 6 months is it safe to assume you are already a japanese national or have a visa lined up?
You might find the working holiday visa useful however you cannot transfer it into another visa after it expires.
The embassy in Perth is quite helpful with WHV, unlike other things.
Buying food and drink for living shouldn't be expensive so long as you are not always going out every night.

Regards