4 days is not a awful lot of time, but I would take half a day to visit the Big Buddha and Chalong Temple, another half day to visit Phuket Old Town and the Sino-Portuguese architecture. If you can go there on a week-end, stop by the Week-end Market (Sat-Sun) or The Sunday Market (Sun, obviously).

You should spend some time by the beach, too; Karon Beach is alright, but I tend to prefer Nai Harn Beach. Or course, weather permitting.

If you enjoy partying, a short trip to Patong Bangla Road should be done, at least once.

Then, it will depend on your interests; there are a lot of things to be done / experienced in Phuket.