You should plan it this way. I have been there multiple times, generally I go to Phuket for 1 day and visit the beaches and enjoy the culture. I spend two days at Krabi because it is less crowded and its a more chill place to be eat. The party scene is very good at Krabi and is certainly better than the other two places. I suggest that you go to Phi Phi Island for 2 days because there are a lot of activities over there ranging from full one day kayaking tours, to parasailing and island snorkelling. It is paradise for beach activities. You can easily skip Chiang Mai and enjoy the beaches. You can explore Thai culture is Phuket too but you can't enjoy beaches like Phi Phi anywhere else.