The small Koh Taen island (you will also often find the name of Koh Tan but it is pronounced 'go tèn' so this spelling is more correct) is about twenty minutes by boat from the south of Koh Samui island opposite to Thong Krut or Bang Kao, the two departure points of the longtails boats to get there. Very close to Samui, this is the number one destination for snorkeling around Ko Samui. The island is bordered by a reef where many multicolored fishes live.
A little further on, Koh Matsum (or Koh Madsum) offers pretty beaches with a lagoon with turquoise waters. On the main beach, there is a small bar where the longtails boats systematically drop you, a little sad as there are much more deserted beaches on the other side of the island. The purpose of this excursion is, as for me precisely, to make an tour away from mass tourism. There is also a cave with giant bats on one of the two islands.
If you get get there by yourself (see below), I recommend this tour to Koh Taen et Koh Matsum for a more pleasant and full experience.