Like Koh Samui, Koh Phangan has beaches that are a tourist draw. Semi-secluded Haad Yuan beach provides a nice alternative to the madness of Haad Rin, especially as this remote beach can only be reached by boat or a particularly adventurous off-road driver (there are no roads connecting these two).
A little easier to access, Srithanu is located about 30 minutes from the pier and main tourist area. It provides a perfect balance of comfort and quiet with several good restaurants and small seaside bungalow resorts. It's easy to find transportation to other parts of the island, but quiet enough that you feel you have a little piece of Phangan (almost) to yourself.