My 11 year old son and I spent our last night in Japan here. It was the most memorable part of our one-week trip, and a very relaxing way to end our vacation. Wonderful spirit, great accomondations, nice gardens, super food. No complaints (except for lack of internet access).
They speak very little English and assume you know the rules (we were the only westerners in the hotel that night). If you haven't stayed in a Ryokan before, read up so you know what to expect (and what is expected of you), as they don't explain much.
Atami is three quarters of the way from Kyoto to Tokyo, and I picked it for our last night to avoid the long train ride from Kyoto to Narita the day of our flight. But in fact, the trains that stop in Atami are much slower than the express trains from Kyoto to Tokyo. From a practical point of view (getting from Kyoto to Narita), breaking up the journey at Atami makes less sense than you'd guess from looking at a map. But as a soothing way to end a trip to Japan, our stay here was perfect. We didn't explore the Atami area, but it sounds as though it is worth an additional day.