We stayed at the Karuizawa West Prince Hotel. I would only recommend this place if you are here to do some skiing - you can walk to the slopes which are nearby.
If you are not indulging in any snow activities however, the Prince Hotel would probably bore you - quite a bog standard hotel with no hot springs. They do have hot springs nearby but charge something in the region of
2000 yen just to use them - and you need to take a shuttle bus to get there.