Everyone's first instinct after booking a cruise is to look at shore excursions, but I think you don't really need a tour in certain ports of call.

The places cruises go is top reason people book a Royal Caribbean cruise, so it seems natural to want to find a great excursion.
However, some islands or cities really don't need an organized tour to be properly enjoyed. While you could certainly explore any port on your own, I think there are a handful that truly are best for walking around and exploring on foot.
While it may not be a mistake to book a shore excursion in these ports, I think you could easily skip them and still have a great time
Perfect Day at CocoCay

While Royal Caribbean's marketing team loves to emphasize the "Perfect Day" element of the name of its private island in The Bahamas, but there is truth in that it's designed to offer what you need.
Royal Caribbean sells a number of shore excursions you can take that are off the island, such as kayaking, swimming with pigs, glass bottom boat ride, and more.
There's nothing wrong with these tours, but there's so much to see and do around CocoCay that is included with your cruise fare that I really don't think you need to book an excursion.

There are different beaches and pools you can go to around the island, plus activities too. I'd save your excursion money for another port of call, such as Nassau, where it really benefits you to have an organized tour booked.
What I'd recommend doing is disembarking your ship early to get the best spots at the beach or pool.
Head to either South Beach or Chill Beach, and get the perfect lounger.

Your plan should be beach in the morning, lunch mid-day, pool in the afternoon.
There is complimentary tram service around CocoCay, so just hop on at your leisure. Or, you can walk it too. One advantage of the tram is you can use it as a way to scout out the areas and find the perfect vibe for your family.

You should treat CocoCay like an all-inclusive resort day. Unless you have your heart set on an excursion that you cannot do anywhere else, I'd stick to what is available around the island.
Rest assured that you can have a full, relaxing, and exciting day without spending a dime on excursions.
San Juan

One of my favorite places to visit in the Caribbean is San Juan, Puerto Rico, and it's also one of the most accessible too.
Your ship will dock in the old city, and you can literally walk off the ship and be there. There's no bus or shuttle service needed.
Old San Juan is built on a hill, so you can walk around at your leisure and see pretty much everything.

"What if I get lost?" Well, you really can't, because if you walk downhill, you'll run back into your cruise ship.
If you're an American, your cell phone will work here too, and that makes it easy to Google Map everything.
Moreover, the sights and historical places are all easily reachable on foot.
Many European cities

I'm headed to Europe for a couple of cruises this summer, and it's become apparent organized tours can be skipped in many of these ports too.
Cruise ships tend to dock in major cities, and from there you can easily get around on foot and/or public transportation.
Most of the excursions offered by Royal Caribbean are essentially glorified bus tours that show these places, but you can easily come up with a walking tour on your own with a little bit of research and jotting down interesting spots.

In each of the cities my ship is headed to, I started a spreadsheet and wrote which places I want to see. Later, I assembled them in order so I can hit each easily.
To be clear, not all European cities are good to skip a tour.
A port that has long transport time between the ship and city (i.e. Rome or Paris) would be one I'd still book a shore excursion for.

Likewise, Norwegian fjords can sometimes be more than a walk away, and an excursion makes sense there.
The important takeaway is to not assume that you need to book an excursion. You may find more choices and flexibility going on your own.