+1 on Nagasaki, or all of Kyushu for that matter. Flights from Tokyo to Fukuoka or Nagasaki shouldn't be too bad. I usually use the JR Rail Pass but you may or may not want it. Should be warm in late April.
I also fell in love with Hokkaido but don't know what the weather conditions would be like in April, I was there in the fall. Probably still cool. Even if you don't go to the northern part of the island, Hakodate and Sapporo are interesting and accessible.