Ride the whole island chain in one sitting - Koh Tao, Koh Phangan, then Samui's palms rising out of the afternoon haze.
Find a room before you go.
The catamaran from Chumphon threads the entire Gulf chain - it is both transport and sightseeing tour. If seas are rough or times don't fit, the landward alternative via Surat Thani and the Donsak car ferry is steadier if longer.

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About four hours with two island calls - stay on deck for the approaches. Morning departure recommended so delays never threaten your Samui evening.
Bus or train down the coast, then the big Donsak ferries. Longer but more departures and calmer water in the monsoon months.
The same ticket price splits into stopovers - many travellers turn this leg into a week of three islands.
Step-by-step transport guides for this stretch of the Gulf coast.