Cherry Blossom Japan: How to See Them Without the Insane Crowds (and Costs)?

I'm desperate to plan my dream trip to Japan next spring for the cherry blossoms, but all the advice points to either sky-high prices or battling massive crowds. Are there any genuine off-the-beaten-path spots or timing strategies to truly experience the magic without feeling completely overwhelmed or breaking the bank? Your insider tips would be a lifesaver!