I just came back from japan last week, and I'd have to slightly disagree with Jonno re. prices compared to the UK at present. Most things seemed about the same or cheaper, with the big exception being public transport which is incredibly affordable and fantastic to use. I think we in the UK have absorbed a spiralling cost of living quietly and do not realise that we are now an extremely expensive place to live.
If your daughter intends to travel round between cities, get her a JR railcard (details from www.seat61.c0m, follow links). If just staying in one area, bigger places have daily / weekly saver cards for tube and overground.
Eating locally and using the 'family marts' for shopping will keep body and soul together nicely - bento boxes are very filling and much better for you than MacD's.
As far as cash is concerned, I took about �600 of yen for 10 days and came back with unspent notes but I'm not much of a souvenir shopper. However, there are ATMs at most 'family marts' eg 'Lawsons' which seem to be everywhere, so maybe you could ensure your daughter has an account and a card so she can access cash if needed. Most transactions are cash which is odd for such a techno country, but it is also extremely safe to walk round with large sums of cash on your person.
I hope she enjoys the experience as much as I did!