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The Mauna Kea Visitor Center is well below the summit, at an elevation of 2800 m (9200 ft.) In addition to providing information about the observatories at the summit, they run stargazing programs Tuesday through Saturday evenings, 7-10 PM (weather permitting, of course.) Parking is first-come, first-served, and vehicles can be turned away if the parking lot fills up; I do not have a sense for how frequently this happens. Also, when departing at night, watch out for invisible cows.
The summit observatories can be accessed during daytime hours, but they are not designed with the general public in mind. The summit road beyond the Visitor Center is mostly gravel and quite steep. When I visited 10 years ago, at least one of the observatories (the Keck?) had a small indoor "viewing area" where the general public could step inside and look at the telescopes; but there was basically nobody else there at the time other than me and my companions. Finally, note that most rental car agencies specifically prohibit their rental cars from being driven on particular roads on the Big Island, and in most cases this includes the Summit Road beyond the Visitor Center.1
1 It used to be the case that rental cars were prohibited on the Saddle Road as well, which would have put even the visitor center off limits. Thankfully, this has changed, and many (though not all) agencies allow their cars to be taken on the Saddle Road. (And even though it was against the rental agreement 10 years ago, that didn't stop a younger, stupider me from driving a rental car clear to the top of Mauna Kea...)