* look at the rainy season (varies by region). Late May or early June might be wet.
* Cherry blossom season is spectacular in early/mid April
* OTOH, kid's school schedule might conflict with April.
* Both April and May generally have good weather. April is a little more unsettled but there are breaks between storms with beautiful days. Not as much during the rainy season.
* Fewer tourists in late April or early May.