Hilo is rainy year-round — there's no dry season in any meaningful sense. The wettest months are November through March; the relatively drier months are June through September. But even in the dry season, rain showers are daily events. Bring rain gear whatever the time of year, and accept that plans may get wet.
The best timing isn't really about weather: if you want the Merrie Monarch Festival (the world's most important hula competition), book far in advance for the week after Easter. If you want Hawaii Volcanoes National Park at its most dramatic, ask the park about active lava conditions before you go — volcanic activity varies considerably from year to year. October through December tends to have the clearest skies for Mauna Kea stargazing, but that too is variable. Hilo's advantages — lower prices, fewer crowds, more authentic feel — apply throughout the year.