We took twice the tour with the same company but there are others too to choose from. Just Google "Star Gazing on the BIG Island" and you will find them. We were disappointed with our second time around so no longer recommend them.
We had quite a bit of snow one year and saw locals skiing down the mountain, Mauna Kea, in HI.
It has to be dark to see the "Milky Way". In other words no moon at all and it has to be a clear night too. Our first trip was perfect. We had friends with us from Europe. They loved it plus the volcano being active, of course.
It is very cold on top of Mauna Kea so be prepared. They will give you Parkas to wear and gloves but your feet are cold if you wear sandals without any socks. Woolen hiking socks will keep you warm even with open sandals as that is what I wore.