[GoNative]

I would suggest looking at somewhere like Hakodate in Hokkaido. Although the winter is not exactly short the town doesn't get a lot of snow and it's about the shortest winter experienced anywhere in Hokkaido. It's also a very beautiful city with a lot of interesting history and there's plenty of places for outdoor activities close by. It's probably a bit more humid than further north in Hokkaido but nowhere near as warm and humid as most of Honshu.
And Hokkaido is one of the cheapest parts of Japan to live in.