Not the most obvious to Western visitors, but by far the commonest activity for Thai and Chinese tourists to the island is sitting in one of the "Skylab" three-wheelers for a tour of important sites. There are two basic tours: everything but Thamphang and the south end of the island for B150, or the Full Monty for B250. Your driver will wait for you at each place, or come back to pick you up if you mean to stay awhile, for example to climb up to the Chinese Temple or carry on to the Buddha's Footprint.
Whatever your plan is, agree on a clearly defined itinerary and price before you set out.