Changing money in Phuket is a street-level business. Independent booths and the recognised Thai exchange chains keep counters in Patong, Phuket Town, Kata, Karon and the larger resort centres, post their buy and sell rates on the window, and deal in cash in the major currencies. Rates move through the day and differ from counter to counter, so the window board is worth reading before you join a queue.
The pattern across the island is consistent: booths beat hotel reception desks, and both beat the counters in the airport arrivals hall, where convenience is priced in. A short walk off the beach road usually buys a better rate than the first counter you see.
Bring your passport. Exchange counters are required to record identification against the transaction, and a photocopy is not always accepted. Count the baht at the window before you leave, keep the receipt if you plan to change money back, and expect a poorer rate on worn or marked notes. Thai ATMs add a fixed fee to every foreign-card withdrawal on top of whatever your own bank charges, which is why many visitors carry cash to change rather than drawing baht at a machine.