Oh, I hope you have a good time!
In Japan, the crime level is very low, but that doesn't mean that one should be oblivious to everything going around them (of course).
A good way to keep your costs down is to stay at a hostle. A famous one in Japan is Sakura House, it is a national chain and they serve good cheap food and have programs for going and seeing things in groups. They also seem very clean.
As for a job in Japan, that might be alittle more difficult to do if you are wanting to travel around. You would first need to apply for the appropriate visa (Samokan put some really helpful links about visas on this thread:
http://www.japanforum.com/forum/japa...resources.html)
Then finding a job for just a short amount of time would be another issue, but probably not impossible.
One thing that may be a good idea is teaching English to get paid (JET, NOVA, google :P) But, of course, you would be tied down a little more on I know for sure JET requires a BA or BS.
As for travel, I started a travel tip thread,
http://www.japanforum.com/forum/japa...-tip-page.html
That might help you alittle more...
Ask more questions, lots of people on here can help!
Thats all I can think of right now :P