If you're looking for a place off the proverbial beaten track, try Kakunodate in the Tohoku (northern Japan) region. It's Tohoku's premier cherry blossom spot -- famous for the Hinokinai River, which is lined on both sides with the most gorgeous cherry trees you've ever seen. Unfortunately (or fortunately, depending on what you like), Golden week (late April/early May) is one of the best times to go. See http://www.japan-guide.com/e/e3601.html and http://www.japan-guide.com/e/e3600.html for great pictures and more info.

Kakunodate is also famous for its samurai district and for a wonderfully delicious sugar candy, the name of which escapes me at the moment...