Wheather you arrive through the airport or ferry pier it is easy to take a taxi from there to Lamai area for 800 THB. Searh google for Villa Whitney and you will be guided directly to the villa.

https://g.page/villawhitney?gm

There are no any public transportation on the island except "tuk-tuk". The taxies are very often to meet. But the advice is to rent a bike or a car.. So you will be able to moove to any point at any time.