OK a disclaimer first of all as a friend owns one of the villas there (which is managed by the resort).
Aleenta Resort, just over the bridge from Phuket itself onto the mainland (Kohk Loy), about 20 mins drive from Phuket airport. Absolutely stunning, unobstructed views over the Andaman, and a cracking - if quiet - resort. There are rooms and suites in the main building, and detached villas on the beach itself, where we stayed.
Well away from the dross that much of Phuket has to "offer", but as I said it is quiet and you might feel isolated. Usual excellent standards of Thai service. There is a good restaurant there but not much in the area if you want to take a stroll somewhere else for dinner (another resort a few hundred yards down the road is all that sticks in my mind).