Shirakawa and Takayama are really amazing, especially in winter under the snow. At the same time, it is not that easy to travel around Shirakawa-go in February, as public transportations are limited. Renting a car is almost a must...
There are many areas that might be attractive for children. In Nagano-ken, there is a famous hot spring where monkeys are bathing - Jigukodani www.secret-japan.com/forum/viewtopic.php?t=496
You could also head south to Kyushu, or even better, Yakushima, where nature is at its best!
In fact, there are many places "off the beaten tracks", and this is what this forum is about! I can only suggest you to read our guides, until you find an attractive option for you.