I would like to rest with my wife and daughter in a quiet island in south Thailand, bungalows near the sea, not too expensive, easy to reach from Bangkok airport ... which one would you advice me ? does it exist ?

You didn't say when / what season - makes a big difference. From Bangkok there are flights to Ko Samui, Krabi, and Phuket. Ko Samet is 3-4 hours by taxi/boat from BKK.

On the northwest point Koh Phangan there is a lovely resort called Wild Orchid (or something Orchid) and another next door. I spent 2 weeks there last spring and found it to be ideal for peace and quiet - most of the time I was one of only a few guests. There are about 40 self-standing bunglows each with a porch and a hammock. As the name implies, the grounds are covered with orchids. There is a long stretch of beach with a very slight grade (good for youngsters) and fair snorkling. Sometimes you can get massages on the beach and there is a SCUBA outfit there but it was always closed. The family that runs the place is very friendly (the dad's name is Mot) and most nights I spent watching movies with them in the dining area. One word of warning is that the resort on the little island across the lagoon has no power so they run a generator at night until about 10pm - I didn't really mind it after I got used to it.
Although the southwest point of the island (Hat Rin) is a zoo because of the Full Moon Party, the northern end of the island is quite peaceful.
If these links work, you can see photos...
http://www.facebook.com/photo.php?pid=48891&id=511642334<BR>http://www.facebook.com/photo.php?pid=48892&id=511642334

A second choice... on Koh Tao on the western side of the island is a small beach / lagoon called Ao Leuk. While it is relatively pricey compared to other options on Koh Tao - and certainly NOT A LUX resort - it is worth mentioning as a good place for families. When I stayed in Ao Leuk, there were a couple of families with small (well behaved) children. My impression was the moms felt quite at ease since the beach is small and not very populated, the surf is not a concern, and bungalows are very close to the beach. Ao Leuk has some of the best snorkling on the island. The one downside is that it is far from everything else on the island and the road is more like a landslide than a road so you are locked in to eating dinner there (the resturant is on a cliff with a breathtaking view of the lagoon). You can take a long boat from Mae Haad (where the ferrys from the mainland stop) or you can take a taxi.
If you SCUBA, Koh Tao is the place to go during the spring (Adaman Sea is too rough after May)
- samui.org/kohtao has more info/photos