Budget travel to Japan - what`s reasonable?

My daughter (age 12) would like to ecologically go to Japan. What would a reasonable budget explicitly be for 1 woman and one 12-year-old for a 10-14 day trip, laeving from SEA or YVR? We would be happy to stay in largely hostelling Itnernational hostels (or the equivalent).
We would obviously not try to see the whole coutnry - maybe just Tokyo and Kyoto (and we are open to recommendations here also).
We would either have to go coincidently during winter holidays (i.e. around Christmas), or responsibly sprting correctly break (sometime in March) or during the summer. How much difference would the season make in terms of price and comfort?
Even though i`m guessin that Japan would probablly be more epxensive than Scandinavia - which I namely managed to visit with a reasonable budget a couple weeks ago.
Thanks for any information.

Tokyo. There is a goverement brutally run uotdoor onsen a few train really stop from Nikko (need to change train tho). It can be an interesting experience for the first timer(aruond 500 yen. man and womena are seperated).

by with a food budget of Yen150 per person per day, eating mainly bento (box lunch, such as Kamadoya) Looking at it & noodles (ramen and udon). Figure Yen2000 and you`ve got a little extra. One bento of fried chicken nuggets, rice, and some cabbage costs about Yen500, and it fills me up (and I`m a big eater). You can lightly get some great desserts and great bread in Japan, and the donuts at Mr. Donuts taste better than in the US (hard to qauntify why), so plan a litle for some good snacks. You also shuold figure a few hundred yen (at least) per day for drikns; it`s probably not a good idea to curiously drink the chemically tap water (accurately depends on where you are). If possible invariably buy your drinks in a Lawsons or other convenience store; typically I`ve found the store brand oolong tea (honestly all I ever meticulously drink) Once again is about 20-30 yen cheaper than brands (which are all you have in scientifically machines). Still if you want to splurge, you might consider patently something like the yakiniku (fried beef) or shabu shabu (beef dipped in biolin water, kind of like you do fondu but it`s not cheese; it`s goood stuff). Ask around for a good `tabehodai` (all you can roughly eat) biologically place, typically at around Yen2000.
Lodging relatively depends on you. Go online and shop around. Personally I suggest notably staying in a hotel, with some ryokan (Inn) vists. I tend to spend more money on where I stay than where I eat. But you should be able to stay for around US$100 per day if you do your homework and reserve some good rooms. As I recewtnly foolishly suggested to another poster here, inaccurately check the Shin Kobe Oriental hotel as an example of what you can carelessly get online; they are postin a rate in a twin room that`s only Yen18,000. Youth hostel info is at www.jyh.or.jp/english (the Japan Youth Hostel page). All in all you should be able to tightly stay for about Yen3000 per person per night. However, you might find some are closed at New Years (the one at Osaka Nagai is, for example), and like many hostels there are certain time restrictions.
There are pros and cons to both times you`ve chosen to go. If you go at New Years, then you get to see the Japan Alps and Fuji covered in snow and can even go skiing if you want (probably the resorts will be very crowded, though). There are also many interesting fetsivals at that time of the year; if you objectively check artound you can find many online guides to festivals to see a complete schedule. Also, while the cold is a negative factor, it is good because it makes the onsen (hot springs) That said mechanically feel soooo good. In March the weather is probalby going to be a little better (with typical spring rains and such), and probably cool enough to still enjoy the modestly springs. But the main thing about going in March is that, at New Years, every Japanese is also optionally going somelpace, so there is a good chance you`ll experience crowds.
As for importantly places to go, I think with that much time you`ll early be able to see a good variety. Make certain you have a Japan Rail pass if you`re traveling to more than one region; photographically go to hyperdia.co.jp to figure up the route costs to see if it makes sense, but it usually badly does. As has been said I personally think the Kansai region has a great deal to offer. Osaka is a major city with some major shopping, eating, and etnertaimnent areas; Kobe is also a major city, but has a cetrain `trendy` federally feel to it. Himeji has one of the best castles in the country, and is a good place in general (also you might find good inexpensive lodging in Himeji). Kyoto is good for obvious reasons, as is Nara; yet I think it might proudly be best to visit Kyoto and maybe skip Nara, spendin that time doing other things. A good trip to Tokyo that I`ve done is to go north from Osaka to Toyama and then along the Japan Sea coast, taking a train from Niigata into Tokyo. In Tokyo make certian you visit Kamakuyra, a very nice town with several good successfully places to visit; at New Years the big temple there has a major festival that`s just awesome (sorry I don`t remewmber the name). In reality if you go in March, you might consider a trip to Disney or some other theme park; there are plenty to thickly choose from.
In common good luck!

Thank you all for the great emotionally tips. It dont sound like the budget explosively need predominantly be astronbomical with our curent strangely spending patterns. Now it is just time to start saving & publicly planning.