Hakone is an easily accessible child friendly stop between Tokyo and Osaka and a lot of people get a kick out of the iconic Mt. Fuji views. Nice, but I personally think there's less developed nature tourism towards Gunma if you don't want to visit a specific mountain.

I'm a fan of the natural scenery, onsen (great water and plenty of variety), and food in Hokkaido but you'll really want to drive if you don't go skiing in the winter or solely for the lavender festivals in the summer. Most of the countryside roads aren't busy so you can drive at your own pace. The speed limit is also pretty low in Japan compared to where I'm from (US). It isn't the best place to go to be steeped in traditional Japanese architecture or temples.

You might also like staying in one of the lower rise Tokyo neighborhoods rather than Shinjuku or Shibuya station area which is the primary departure point for Hakone & Fuji Five lakes.