Miyazaki enjoys a fairly mild winter climate and there's a fair amount to see along the coastline. (A car is best. Train schedules are pretty hit or miss.) But Izu Peninsula is also nice because you can catch the early blooming cherry trees. I can't say it'll be really warm, but it will be pretty!
February is usually the coldest month in Japan, in my opinion. However, within mainland Japan, I would recommend going to Shizuoka prefecture, preferrably in Shizuoka City. While it gets a negative in Tokyo, it's still 0 - 2 degrees there, and the good thing is, it never snows in Shizuoka City because it is well protected by several mountain ranges. So while the other neighboring cities are snowing, these mountain ranges stop the snow from crossing the border to Shizuoka City.
Another place in the same prefecture that is nice to visit is the Izu Peninsula just beside Numazu City, where you can get a great view of Mt. Fuji with its snow capped peak.