It's worth making your way to Hua Hin, since it’s a beautiful seaside city with opportunities to visit an elephant sanctuary (rescue centre- you can’t ride them, but you can clean them!)
I recommend starting in Koh Samui. It’s a beautiful island and the perfect place to rent out a moped and take a day to drive the full way around it. It only takes an hour.
Getting from Koh Phangan to Koh Tao is simple. There are lots of options, and you’re the best bet is to ask and search around book online. The ferry takes between 1 hours to 2 hours depending on what speed you choose
This is another boat journey (I hope by now you don’t have sea sickness ),but it also is a bus journey to drive you to the other side so you can check out the NEXT set of islands
These islands are well known because of two things: James Bond island (speaks for itself) and Phi Phi Leh, ie The Beach island, famous for featuring in the Leonardo DiCaprio movie, the beach