The hotel is likely 35 minutes minimum from the airport without any traffic. I'd budget an hour to be safe. I recall the fixed-price airport cars to Kamala being about 600 or 700 baht. A meter taxi would be a bit less if the driver knows where the hotel is and takes you there directly. I suggest googling some. Taxis in Phuket are a little different than most places in the world. I'd plan on taking in the sunset at the hotel if your timings are really good, particularly if you have checked luggage. Bear in mind that the hotel kind of faces north i.e. not direct sunset over water views. You could take a taxi home if you time the shuttle to get to Kamala town almost immediately after arriving at the hotel. I genuinely like the hotel and think the staff is awesome in terms of friendliness and hard-workingness despite many of the tripadvisor reviews I've seen. If you're overly worried about taxi costs, you'll likely leave a visit to Patong on a one-night stay at the Hyatt with regret.