[Maku]

If you're thinking of travelling there on a budget, you should think of spending as little getting there as possible too.
That's why, when I head over there, it would be cheaper for me to go to Slovenia first, then onwards to Japan.
If you look on the right sites, you can save as much as £400 GBP.
Also, accomodation prices vary quite broadly depending on where you will be staying.
Large towns and cities are more expensive, as with every other country, but there still may be a chance that you will find the odd cheap place to stay if you look at the sites provided by previous posters.
The food question can only be answered by me after looking in the Japanese store and the Japanese restaurant in my town, which is hardly anything to go on so I wouldn't really trust it if I were you.
From what I've seen, foods without meat, fish or eggs are not uncommon, but they will come at a price.
To live off a budget for me in your position would mean mainly rice products e.g. onigiri, but then again I don't really take to having 3 set meals per day, so I'm not sure if this will be of any use to you.

And to answer a question just asked, $1 = 123.877 Yen at present, according to XE.com.