[QUOTE=spike74]It costs about $425/night for the two of us including dinner and breakfast so cost is the reason why we haven't just booked the two nights in the Ryokan already. If we only stay one night in the Ryokan, we would spend the other night in a Western-style hotel.
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I won't for a moment try to put you off a Ryokan experience - I'm truly envious and just wish I could afford one myself!
So far I've had a 'budget option' in a beautiful old building that USED to be a Ryokan with gorgeous stone onsen, but where the owners weren't able to provide the glorious meals and service (although the food was very nice!). The cost was about 70$ a night each.
It was in the Taiyo-Sanso in Gora, in Hakone, and I wish I could tell you the contact details but I can't find any mention on the web, and I've lost my old notebook - sorry! (nope - I've found it again!)
If you're looking to hang on to the Japanese experience for a bit longer before settling for a soul-less western room, then you could try the state subsidised versions of ryokans - kokumin shukusha
There is a website (all japanese, alas) with lots of beautiful pictures of what's available:
http://www.kokumin-shukusha.or.jp/

However, you can use this WONDROUS website to open it (or any other japanese pages)
http://www.rikai.com

As long as the characters are 'written' into the web page (rather than images) you will get an instant translation just by hovering the cursor over a word. It's an amazing tool.

I do hope you have a lovely time (just don't get a taxi from the airport - it will ruin you!).