I've not stayed there (only eaten at the restaurants) but the Sanuki Club in Azabu Juban has reasonably priced rooms with a bathrooms on each floor and a large shared bath in the basement.
http://www.sanuki-club.com/English/top_english.htm
Not so long ago the wonderful Koshino Yu neighbourhood onsen was just a short walk away - alas this facility closed down

A very cheap option in a convenient location is the Lutheran Centre in Ichigaya which will give you a large room and access to shared bathing facilities (under 7,500yen for two)
http://www.l-i-c.com/english.html

You might also like the Andon Ryokan near Minowa station - not such a convenient location as the other hotels I've mentioned, but definitely workable. They don't have a sento in the traditional style but a jacuzzi in addition to the showers - http://www.andon.co.jp/bath/index.html (doubles from 8,190yen)

Although I've looked into them, I've never stayed at a Dormy Inn as I can always seem to find something that I consider to be better value for the 10,000yen or so it costs for two people.

I'm a big fan of neighbourhood sento and onsen (although my husband absolutely is not), if you haven't seen it already, you might get something out of this thread:
http://www.flyertalk.com/forum/japan...kyo-onsen.html
(the thread also includes information about this super-onsen in Osaka: http://www.onsen19.com/ )

For Kanazawa, jpatokal recommended that a friend of mine stay here:
Ryokan Shibaya http://www.yadotime.jp/shisetsu/12/index.php
http://www.flyertalk.com/forum/japan...l#post11206214
The reports back were good and rates were cheap and included breakfast.

Another suggestion (which also has a shared bath) can be found here:
http://www.flyertalk.com/forum/11231303-post15.html