Most nights I wore either cargo type shorts or khaki shorts along with a collared polo type shirt. The wife also wore shorts and a blouse of some sort. The only time we got more "dressed up" than that was when we went to Otaheite. Most men wear khakis or linen pants and a button down shirt with a collar (can be short sleeved). Most women wear a skirt or dress of some sorts. Some really like to get pretty fancy, but its not at all necessary.
The dress code only applies to restaurants. During the day, swimwear is acceptable for either of the restaurants, Beach Grill and Cassava Terrace. Both are open-air restaurants. At night, Lychee, Cassava Terrace (buffet by day, a la carte by night), and Heliconia (Beach Grill by day) are resort casual, which means shorts (or jeans), shirts, and sandals are acceptable for both men and women. No swimwear allowed at night. Shirts and shoes must be worn. Otaheite, which is the only "reservations required" restaurant at CN, requires men to be in collared shirt, pants, and closed-toe shoes. Women are usually pretty good about deciding what outfits fall into these categories, but, as a reference, a sundress is acceptable pretty much anywhere at night, and the closed-toe shoes are not required for ladies. I bring one pair of long pants and casual dress shoes for Otaheite and she brings a nicer dress and shoes for that night (we usually eat there only once). Other than that, it's shorts, sandals, and polos or resort-style button-ups for the other nights. I don't think we ever wear anything but a swimsuit until at least 5p on any given day. Hope that helps!