Get the local bus, only costs 100 baht, and takes about 2 hours.
Then when u arrive at the bus station ( it stops at 2 in Phuket, you want the last, where it terminates, unless you want otherwise.)
You can then catch a taxi to where ever.
I was going to patpong, 500 baht for the 2 of us. I can't comment how much to any of the other beaches.
Many of the tour desks will charge you 2000 each. Even then, they will take you somewhere then stick you on the local bus ( I know, happened to me few years ago)
The hotel security will flag the bus down for you if u ask them, think it's every hour or every half hour they run.
So what would potentially cost 4000 baht for two of us......actually cost 700 baht....what a bargain.
A great way to mingle with the locals, and most of the buses are very comfy.
And the same applies in reverse...phuket to kho lak .