"Chichu Art Museum" is the most popular tourist attraction in Naoshima. Distribution of "waiting numbers" is finished at noon during peak-season.
If you go there during peak-season or a daytrip to Naoshima, you should get a web tickets in advance.
The museum displays artworks that you should see once such as "Time/Timeless/No Time" by Walter De Maria and "Open Field" by James Turrell.
I recommend you to visit the museum if you trip to Naoshima.