Although most Thai islands are crowded and sometimes overrated/priced they are surely worth a visit. For us the most memorable stay must have been on Adang Island, part of the Tarutao National Park, this small island located in the south of the Andaman sea near to the Malaysian island Langkawi is absolutely beautiful. There is no commercial accommodation located on the island, only government run with limited capacity so the island is never overrun. If you want that moment alone on the white sandy beach, this is the place! Snorkeling just of beach you can see clown fish, some lovely corals. Even better is when you rent a long tail for the day and have them drop you at various stunning sights.
We made our way up to Koh Lanta, which we didn't find so appealing. If your looking for long sandy beaches with door to door beachfront restaurants and bars this places fits the bill. Even more up north we stayed at Railay Beach, this spot is stunning and dramatic. The karst cliffs surrounding these beaches are amazing. There are a lot of monkeys here, the very common and quite aggressive macaques but also the laid back and beautiful dusky leaf monkeys. Railay is famous for its rock climbing, there are some great places where you can get a introduction into the sport. With all this natural beauty comes a price, its overrun, overpriced in high season so we would recommend staying on another beach and visiting Railay via long tail.
On Thailand's east coast we visited Koh Tao, known for its beautiful dive sites this island lives of diving oriented tourism. We enrolled in an open water course and fell in love with it. The dive sites are as beautiful as they say, we saw so many interesting and odd looking fish. The underwater world is a magical place.
To sum it up: the weather is great, the water warm and sea is clear. The natural beauty abundant. We would recommend staying in the national parks during high season, its cheaper and almost always even more beautiful and far less visited.