I would like to bring a different approach and give an idea of how low one can go in terms of cost. Note that this is not meant to be a comfortable way of travelling, simply a very cheap one. Prices are estimates in USD. Naturally, all this applies mostly only to major cities like Tokyo, Osaka or Nagoya.
(Check out this question for more info):
- Couchsurfing = $0
- Manga Cafes = $10 (Not all manga cafes accept sleepers, but there definitively are. Not very comfortable.)
- Capsule Hotels = $20 (Somewhat comfortable, plus you gain access to showers.)
- Convenience store onigiri = $1 (I found that two onigiri for breakfast did it for me.)
- Convenience store bento = $5-10 (Plenty of choice, plus you can get them heated.)
- Izakaya = $15-30 (This can make for a nice and fun supper, choose your dishes carefully as some are expensive.)
- Walking = $0 (It can work if you stay in a semi-small area.)
- Train ticket = $2-3 (This will enable you to move around much more, combined with walking.)
- 24 hour pass = $6 (This will make exploring areas that are too far for walking easier.)
- Exploring = $0 (Walking around the city can be surprisingly fun.)
- Temples/Museums = $0-5 (This requires research, but there are many cheap things to do.)
(If you are a university student like me, take your student card, it is accepted in many places for a substantial discount.)
In conclusion, in the worst of worst scenarios and with amazing planning, you could technically get by with as low as $5-10/day or less than $100 for two weeks. Needless to say, that would suck (a lot), you would be eating lots of only white rice and sleeping in some sketchy spots, but it should be doable for the more adventurously inclined.
A much more reasonable yet still low amount is around $50-100/day ($700-1400 for two weeks), with that, you should be able to have a fun vacation and not be bothered too much by the restrictions.
My friend and I stayed one month in Japan and we spent an average of $150/day with no privations whatsoever. Of course, we were not staying in fancy ryokan every night, but it was very enjoyable and I eat a lot.
Bottom line is: Traveling in Japan can be as cheap or expensive as you want it to be.
You simply have to make decisions accordingly.