I have stayed at the Hilton in Karon, the Kata Beach hotel in Kata, and the JW Marriott in the north. None of those hotels could be described as 'cosy' though.
A budget of up to $150 will get you very far in Phuket. In my experience even the 5 :-: hotels are around $100 (the Hilton is less and so is the JW if you use Priceline).

You should also try a search. Phuket hotels are discussed a lot.