Nick, It depends totally on what kind of "ryokan" you are looking for.
The *original* definition of "ryokan" is the rather expensive Japanese traditional inn, where you (normally) get your dinner served in-room, an attendant comes to your room to lay out your futon beddings and such, and often the inn comes with a very nice, large hot spring bath. If this is what you are looking for, then Motoyu Ryokan as suggested by saiji is the one you might consdier, though they are expensive.
http://www.motoyu.co.jp/
The more recent use of the word "ryokan" is to refer to budget Japanese-style inn, often family-run, with simple tatami-mat rooms, sleeping on futon which you lay out by yourself, shared bath (not necessarily hot spring water), dinner may not be included (Sawanoya does not serve dinner), and friendly to your wallet. More like B & B. Sawanoya recommended by mimi is of this type.
http://www.tctv.ne.jp/sawanoya/
While either has its charms (and different prices), I just don't want the original poster to expect for former and end up with the latter, thus the explanation :)
