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The fastest and easiest way is by plane. The island has a tiny airport, making it possible to get there within 1 hour from the north or south of Thailand. The prices for a flight to Koh Samui are the most expensive within Thailand. You can plan on about 100 € per person. It is worthwhile to travel by plane from Bangkok or Phuket. But always keep in mind that with a flight many impressions are lost that you could have by bus and boat. So booking a flight is for those with little time. Also, once you arrive at the airport, the fare to the centre is much higher (500Baht 10 minutes). Regularly there are shared taxis from the pier for about 200Baht. It is not worth looking for a cheaper taxi, the prices are agreed between the drivers.

The journey from the surrounding islands is easy due to the mass tourism. There are daily trips to the neighbouring islands, towards Phuket in the south and towards HuaHin in the north. When you arrive in Koh Samui, there are already a lot of shared taxis waiting that charge about 200 baht.

The top/hot spots are Chaweng Beach with the Central Festival shopping centre, and a little further south (5km) the village of Lamai, also with a sandy beach.
In the evening, Chaweng alone is interesting. A larger tropically designed club (Green Mango) and many restaurants and typical tourist amenities.
There is a lot going on in Chaweng, Lamai is rather quiet. Fishermens Village in the north is good for eating out but also more expensive.
Young people are almost exclusively on Chaweng beach. This is a long sandy beach around the haleb east of the island. A small main road (one-way) runs the length of the beach. Very convenient all and easy.
The road traffic is acceptable and concentrated in these two places and there only the main road along the beach in each case.
Both places are very well suited for all target groups. Mainly couples feel comfortable in Chaweng. Loud music is only concentrated in 3 small areas. On the beach the Ark Bar, on Chaweng Lake the red light district and at the GreenMango discotheque. Everything else on the island is tropically beautiful and relaxingly quiet.

If you can drive a small motor scooter yourself, you absolutely must rent one of these for 150 baht to 200 baht a day. Hand in your passport, take photos of old damage to the scooter. Then put on the helmet and drive around the island. Like everywhere else in Thailand, the roads are dangerous, be it slippery sand or road damage. Therefore, drive calmly and slowly. With this scooter, you can save yourself all the tours that are sold, because you can drive there yourself and dont have to adapt to the tour schedule.

Sleep well, eat well, walk to the beach and take a leisurely trip now and then. If you want to party, take advantage of the weekends on the beach with a connection at the open disco (Green Mango) just a 3-minute walk away. During the day you can visit a typical temple, the pool on a smaller mountain called High-Slide including shaded areas, eat and drink or what the majority does, just eat an ice cream in Chaweng at Central-Festival and then go to the beach around late afternoon. Have fun :)