Must...wear...sunglasses! The sun is bright, especially with sand and water reflections. Don't forget a hat to keep the sun out of your face! It also helps wherever your part is. I get sunburned easily so my scalp peels and it looks like dandruff so I always wear a hat!
If you decide to wear jeans to the beach make sure not to get them wet because they take FOREVER to dry and the one time I did I was annoyed all day long as I waited for them to dry. The water also makes them heavier and when sight-seeing it makes it more difficult.
Especially for children I would recommend water shoes for all those shells and jelly fish parts left on the sand...I had a bad childhood experiment. Shell went right through my foot.
Toiletries and Medical Supplies: Please don't forget your sunscreen! We all know the effects of too much sun-damage on our skin!
Don't forget your water either! Especially in the summer it's very easy to get dehydrated which will lead to heat stroke or worse. I've seen it happen many times. Be on the safe side! Drink plenty of water while at the beach or touring historic parts of the island.
Photo Equipment: Beware that a drop of water can ruin that digital camera. If you're going to take your camera to the beach you might pick up a water-proof case for it. I mean...if you've spent hundreds of dollars on that camera you might as well help keep it working.
Camping/Beach/Outdoor Gear: If you're going to the beach don't forget your towel, suit, etc. If you have kids I'd bring a boogie board in advance or else you'll be buying one down there. Everyone seems to have one and if not they end up going across the street for one.
Mosquito repellent after dark is a MUST!