Sorry- this got longer than I'd planned! Admittedly, I haven't been since pre-covid, but prior to that, went maybe 6 times to various islands over the years.
Why is flying into Koh Samui so much more expensive? The reason behind the higher flight prices than usual is that Bangkok Airways owns and operates the International Samui Airport. Bangkok Airways built the Airport in 1989, that today receives more than 1M travelers per year and is considered one of the most beautiful airports in the World.
The airport is indeed lovely, with majority of it being outside with gardens and palm trees! Kho Samui is a short boat ride to Koh Phangan- where the full moon parties are. Parts of Koh Samui are equally as hectic. We stayed in MaeNam, which was on the other side of the island to the busier, clubby town of Chewang. We recall seeing a large Buddha on a hill and seeing a waterfall, but we mainly went to visit a friend living there at the time.
Personally, I'd hire a car/jeep and never a moped no matter where in Thailand you go! They are the biggest cause for tourist injury and death! Is there anything else you'd like to do there? Scuba diving, rock climbing, relaxing by a pool?
Phuket is the largest island and has the most domestic and also international flights into the airport. It means more frequent flights, more choice or airlines and often cheaper prices than some less known islands. Are you flying direct from Chiang Mai or from Bangkok to the island?
I would avoid Patong beach at any cost! Very touristy, busy, kickboxing tournaments, strip clubs and just not relaxing. Stayed there twice with 10yrs apart and it got busier each time. Karon and Kata beaches further down the coast were quieter, but still have enough food options and nice hotels. The east side of the island is more fishing villages, but the last time I went, they were starting to build some smaller hotels there. Phuket island has lots to see and do. Elephant sanctuaries, big stage show things like FantaSea, the big Buddha and much more.
From Phuket, we got a ferry to Koh Phi Phi for a few nights for a change. You can also get a ferry from Krabi- which also has alot of flights form Bangkok. I went to Koh Phi Phi even pre the tsumami, so can't comment on what its like now. We scuba dived and went to the beach where they filmed the movie 'The Beach'. Sadly, it was covered in rubbish due to tourists leaving it there though!
Although Krabi is on the mainland, its on a beach. There are some more secluded hotels in various coves and its a haven for rock climbers.
A lesser known island on the Eastern side of Thailand and farther north than the others I've mentioned is Koh Chang. We flew into Trat and got the ferry to the island. This was 10yrs ago, and it felt less touristy than say Phuket or Koh Samui at that time. Other than scuba diving, I don't remember doing much else other than swimming in the hotel pool. They did advertise that the Cambodian border wasn't that far and a day trip to Angkor Wat was possible. We decided against it as thought it might be too rushed- but in hindsight, wished we had done it.
Happy to answer any questions, but hopefully someone with more recent experience can advise too.