There's no need to stay in a dorm in Japan.

As long as she's OK with sharing toilet and shower facilities there are plenty of places where she can have her own room (generally, at the very low end of the scale there's not much difference between the cost of a twin room with that of two singles).

The cheapest way for two people to stay is in 'semi-double' accommodation, although you share a bed with this option, you would get your own toilet/bath. It will depend on your relationship and how large you both are.

If you do require a twin, Expedia are running a stay three nights, get one free promotion on some of the Tokyo Hotels. There are two Chisun Hotels (a very nice business chain - Hamamatsucho has, IMO, a better location) that come under this offer where you could get ensuite twin rooms for around 9,000yen (4,500yen each), as long as you stay there for three or six nights. But there are plenty of places with non-ensuite rooms for under 3,000yen.

If you have problems finding accommodation in Kyoto, try Osaka or this place in Nara (http://www.superhotel.co.jp/en/s_hotels/naraeki.html - it has availability, albeit in smoking rooms, on most of your dates)

Sorry I can't look into this more for you right now, I'm rather busy this morning. I have done the leg work already though
http://maps.google.co.uk/maps/ms?ie=...b4a59f856&z=11
All the budget options with shared facilities that I know of in Tokyo are marked with a yen sign

If you still need help, let me know what else you require and I'll do some more later.

EDIT - my findings for Tokyo are:
lowest end singles with shared facilities is 2,500yen to about 3,500yen each

lowest end ensuite semi-double (for two) 5,500/6,000yen

lowest end twin 8,500/9,000yen (about 7,500/8,000yen in Osaka/Nara)