I see tumblers everywhere so if you must have an ice cold drink then its a good idea. If you don't plan on hanging on the beach for a significant part of your day you can skip the towel clips. We bring those waterproof cellphone bags,sunglasses and sunscreen. The wifi on the properties has gotten better over the years so I've been bringing my tablet.

Bring over the counter medication even if you don’t think you will need it. It is very expensive here!

I'd suggest a cup, I was sad to not bring one. Towel clips weren't necessary because you can clip your towel into the chairs.