Help! I'm overwhelmed by ryokan options, and the more I spend researching, the more frustrated I'm getting. (I'm a detail-oriented traveler--what a surprise!--and usually have a much easier time narrowing down options.)

Second trip to Japan for me, first for my friend. We've allotted 3 days to spend outside of Tokyo, and on the last day we need to get to NRT for an 11 am flight, so that limits our travel radius or requires us to rearrange Tokyo travel dates. Right now we're planning to spend May 28-June 1 outside of the city (with June 1 departure from NRT).

Kyoto and Hakone seem like the most obvious options because of location, but we'd be open to other suggestions.

I'd love to stay at a traditional ryokan, and would prefer:
1. A place with great food.
2. Private toilet and preferably an in-room/open air private bath.
3. Some place relaxing after nearly a week in Tokyo
4. Scenic atmosphere (i.e., nice gardens or lovely view, etc.)

We're averaging $300 room nights (2 people/1 room), but realize that we'll have to bump that up for better ryokans.

Does anyone have ryokans to recommend in the $400-500 per room range? Or would you recommend 1 night at a more expensive ryokan then skimping for 2 nights at another hotel?

Is three nights at a ryokan overkill?

I realize that Kyoto and Hakone on a weekend in May are bound to be jammed with people fleeing the city. Any other recommendations for areas still within a ~2 hour Tokyo travel radius that are less touristy but still a worthy destination?

Thanks!