Every season has it. Winter because of the clear view and on not so high destinations also in winter hiking is possible and agreeable.

Spring has the first flowers and greenery to see, in summer also kita alps with 2000m-3000m are accessible while it is too hot for the lower mountains close to Tokyo and in autumn you can enjoy autumn leaves while hiking.

For planning any trip yamareco is a highly recommended ressource which is for free (not as Alltrails or others) and gives you full control about your hike. It's in japanese though but worth the efford to work with automatic translation provided by your webbrowser. It's even possible to export GPS data and then import them to a free mobile hiking application of your choice.