Tuk-tuks - a 4-wheeled variety- operate in all the beach centers and should not charge more than the following fares from June 1st, 2002 - but this is only a recommendation ...

Open air buses are much cheaper but do not go from beach to beach. Their routes go from the beach to Phuket Town and back for 10 Baht each.

A more flexible way would be to hire a car or jeep. Most of the vehicles on offer at the road side in Patong are often not insured and, since vehicles in Thailand are heavily taxed, replacing one you damage will be expensive.
Motorcycles are also easily available for hire, but with the accident statistics in Phuket as high as they are, we strongly recommend that you resist the temptation. Insurance is also not available.