Okayama Station: This is the cleanest rail gateway from Honshu: take the JR Uno Line to Uno Station (about 50 minutes, roughly ¥600), walk across the road to Uno Port, then take the ferry to Miyanoura Port (about 20 minutes, roughly ¥300). From Miyanoura, Honmura is about a 30-minute walk or a short but infrequent ¥100 town-bus ride. Allow 1.5–2 hours from Okayama Station to Honmura after connections; do not cut the ferry connection fine.
Takamatsu Port / Takamatsu Station: From JR Takamatsu Station, walk 5–10 minutes to Takamatsu Port and take the direct ferry to Miyanoura, Naoshima’s main port. The crossing is about 50–60 minutes and is roughly ¥500–¥600. It is simpler than routing via Okayama if you are already in Shikoku, but only if the sailing time works; ferries, not trains, set the day’s rhythm.
Takamatsu Airport: Take the airport limousine bus to JR Takamatsu Station/Takamatsu Port (about 40 minutes; roughly ¥1,000), walk to the ferry terminal, then take the 50–60-minute ferry to Miyanoura. Budget around 2 hours airport-to-island including the port transfer and a ferry wait, and about ¥1,600 before travel onward to Honmura.