Feed the culture vulture within at Awamori Museum. Check if there are any guided tours or ask a museum employee to direct you to some of the highlights.
You'll have sightseeing choices galore when staying in Ishigaki. Awamori Museum is a great place to kick off here, but there are loads of other worthy places to consider. Fusaki Beach, Maezato Beach, and Shiraho Beach are not far from the museum and will top off your day nicely.