With only two nights, I recommend to select a hot spring resort in the Kanto Region. Hakone is the most easily accessible:
http://www.japan-guide.com/e/e5200.html"Onsen" is uniquely Japanese, especially when combined with an overnight stay at a ryokan.
For excellent, sulfur smelling bath water, I recommend the onsen town of Kusatsu, although a bus ride is required from the closest train station:
http://www.japan-guide.com/e/e7400.html
The best onsen ryokan ryokan I have stayed at so far is also relatively easily reachable from Tokyo, but making reservations is difficult because of its popularity:
http://www.hikyou.jp/nagano/seni/seni.htm