Most Sandals breakfast and lunch are fairly casual. Cover-ups over bathing suits, shorts and t-shirts, sandals, etc.
Dinners can be "casual" or "elegant"
Casual: sundress, skirts, dress shorts, polo or button up shirts, etc
Elegant is ... Elegant. Nice dress, nice shoes, slacks for men, etc.
If you check out the restaurant page : http://www.sandals.com/main/royal/rj-dining/
It tells you which restaurants have which dress code, what time they are open and if reservations are required.
For your daytime activities, dress for the occasion.
Snorkel: a rash guard or tshirt will help protect from sunburn
In town: dress neatly, but casual. You don't want to be a target, but want to look nice. Don't bring camouflage unless you have to. Culturally, camouflage has political implications.
Land to water: bring close toed water shoes or old sneakers for activities like Dunn's river falls, horseback riding, zip line, etc.
Bring at least three swim suits, IMO. That way you never have to put a wet suit on...yuck!
Bring a white outfit for the white outfit for the chocolate buffet white night.
Pack at least one bathing suit and one change of clothes in your carry-on. If something happens, or if you arrive before your room is ready, you will have beady access to your vacation clothes.
Likewise, if you are coming from a cold climate or dress in layers for the plane ride, change on the plane.... There can be a long line for arrival procedures and the temperature can be extreme compared to the cooler, controlled airplane atmosphere. Also, everyone else will be rushing to the bathrooms and you will be relaxing in the lounge!