As in Thailand, the islands can get incredibly hot and humid. So, pack a good supply of easily washable cotton t-shirts, tank tops, shirts, cotton dresses, skirts, shorts preferably in light colours.
A couple of long trousers or dresses if you hope to visit any of the surrounding temples in Krabi, such as Wat Kaeo Korawaram, Panurat Temple, and Wat Tham Suea (Tiger cave temple).
Swimsuits, of course, should be an important item. Pack a few extras, so you will have several standbys when one pair gets wet. Coverups such as sarongs and bandanas. A good pair of sunglasses, a nice wide brim hat, and sun protection is a must. A comfortable pair of flip flops while at the beach and sandals for exploring the town and beyond.
When it comes to clothes pack light, as you will no doubt want to take advantage of the amazing shopping available on the islands and the mainland. So, make sure to keep some room and don't overpack. Plus travelling light means easy mobility to discover all the wonderful locations.