One of the best things about a cruise ship are the places you'll visit, and you can make them even better with a few easy things.

Cruise excursions will get you to the place or activity, but they're not going to cover everything you may need.
I think most people understand to bring sunscreen, towels, and other basics. But there are other not so obvious things I'd recommend bringing too.
This list is a result of various things I've seen other cruisers bring and then I thought "that's a good idea". It's not essentials or things you'd have a bad time without. Rather, they can enhance your tour.
I hope some of these might also inspire you and make your cruise excursion better.
This article contains affiliate links that cost you nothing extra to use, but I make a small commission.
Inflatable floats

I had been to St. John a few times, but on my last visit a fellow cruiser packed inflatable floats that are exactly what I wish I had all along.
These floats allow you to sit, paddle, or lay on floats connected by a mesh material. The genius of it is it's inflatable, so you can deflate when you're done and pack it up. Plus, you can use it in different configurations to suit your needs.
I think having it so you can sit in them is perfect for most beach days. It's nice to be in the water without actively swimming. The floats make it easy to sit or lay on them, which allows for flexibility.
Unlike other floats, I like these are very compact when deflated so it's not cumbersome to travel with.
Bluetooth speaker

Bluetooth speakers get a lot of hate these days because how some people misuse them without consideration for others. However, I think there's value in responsible use.
I've been on excursions to the beach where there is a significant distance between us and others. Or we're in a cabana that has some privacy. In either case, having music at a reasonable volume is a nice touch.

If you rent a cabana at Perfect Day at CocoCay, Bluetooth speakers are included (ask your cabana attendant), so you don't need to bring your own.
I'd recommend picking up a water resistant speaker to ensure it doesn't get ruined while at the beach by water or sand.
Portable fan

I've seen more cruisers bringing portable fans with them to keep the air moving.
These rechargeable fans can be the difference between stagnant, humid air and some level of comfort.
They're great on bus rides, waiting for taxis, and generally being outdoors.
At first, I thought they looked too dorky to wear, but then I remembered I really don't care what other people think. My comfort level is more important than impressing random people.
Wet bag

One of the smartest things to buy for a shore excursion is a waterproof bag to bring back and forth from the ship.
This is your portable means of easily carrying towels, clothes, electronics, and more. But it also needs to be practical for the beach and surf. You want something packable, yet useful to carry the necessities.
The two bags a lot of cruisers recommend: Waterfly bags or a Columbia nylon backpack.
It just needs to be a bag that won't get soaked with water when wet, but durable enough to carry what you need. You might even have an old bag at home that does the trick.
Entertainment for the bus ride

This tip is for the families, because keeping your kids from complaining they're bored is a win anytime.
While I might be content looking out the window and enjoying the view, that's nails on the chalkboard for kids.
Since most excursions involve a commute to get to/from the actual activity, I'd recommend bringing something for them to watch or do.

A tablet works quite well, especially if it's preloaded with something to watch, play, or read.
The first time we tried this was on a long bus ride to a beach in Jamaica, and it saved everyone's sanity.