I don’t know how many days you have in Japan, so I’m working with the idea you have two weeks.
End of October – start of November coincides with autumn leaves north of Tokyo and other higher elevations (such as the mountains). The Tohoku region is often said to be the best part of the country for autumn leaves, so I think this would be the ideal time to go. I’d recommend spending a week travelling around Tohoku, you’d be surrounded by nature at all turns, beautiful temples, hot springs and hiking, and visiting traditional towns. Tohoku is generally a rural area and more off the beaten path, so you’d get to know a side of Japan that doesn’t often feature on other tourist’s itineraries.
The second week could be spent around Tokyo, or further south if you’d like to visit Kyoto or other sights.