So while I am mainly focusing on Royal Caribbean and it's ships this is pretty well universal for cruising, taking excursions only with ones offered by the cruise line.
Now don't get me wrong there are certain things that are great about taking an excursion with the cruise line. I personally like to SCUBA dive (for those who don't know it means Self Contained Underwater Apparatus which is why it is all caps) and my first cruise had a dive in Cozumel. The dive was nice and the crew did a good job, in fact I have dove with them since my first time on a ship and will likely go back. However since you must be certified to dive there are no where as many people on the ship who will be going, case in point my first dive had about 30 people total and that was on Liberty of the Seas which had around 3000 people onboard so about 1 percent of the number of people on an excursion. IMHO that is a pretty small number and the only places you will find numbers like that on a cruise ship excursion will either cost a lot, require a ton of effort, or will require some sort of certification. I don't mention unpopular excursions mainly because it's hard to determine which ones will be unpopular and if they are unpopular they will likely get removed as a possibility.
So you know you want to take a cruise and are the type to book ahead. There are a few options and each has good and bad things to think about. One of the big ones people worry about is getting back to the ship on time because there is nothing worse than watching someone running along trying to catch the ship when it's already dropped the moorings. These people are often called "pier runners" by people who see them. This is a major reason why people like to book with the cruise line as if you are on an excursion and something breaks down and you will not make it back to the ship by departure time the cruise line guarantees that you will get back to the ship or home if you book with them. That is a great thing and something we all want to have for the "just in case" that is why we buy insurance (or are forced to in certain cases) because no one wants to be stuck in a foreign place wondering how they are going to get home.
Another thing you often wonder is if the people operating the excursion are professionals or just some random person who offers a tour. Again this is a reason why people book ahead and use the cruise line. Some random guy may take you on a great tour but could also have you an hour from your pier and then start telling you to pay up to get back and no one wants to deal with that possibility.
And a big one is transportation, how do you get from the pier to your excursion. Being in another state let alone another country can make things nerve racking when trying to get around. Do you take a cab, bus, train, boat, etc. to get to your destination. Yep, I said boat as well because some islands offer hop on hop off ferry services fairly close to the pier and it is a perfectly viable way to get around. But figuring that out can be a PAIN which is why I often look for excursions with pickup right at the pier and most cruise lines have this already baked into their programs.
So booking with the cruise line often solves those three things but it adds another one which is crowds. As I said at the start SCUBA diving isn't going to have a ton of people but at the same time it's nice when it's even less and there are places that offer excursions that can be booked outside of the cruise line. I have used them before and it was mostly good. However you may have to find your own travel to the excursion destination though they often offer guarantees that you will get back to your ship even if you have to work out your own travel from the pier to the excursion. You will also have a lot less people going along and I have actually been on an excursion basically by myself with only a guide.
Another option is to just find a place and set up a booking. I did this with my last cruise since most of the pickup points were at or very near the pier but in Antigua I had a 45 minute ride from the pier to the dive operation. It's nerve racking the first time for sure but I was lucky enough to spend 2 weeks in Montego Bay, Jamaica and had taken the local route taxi's so I knew mostly what I needed to do to get around. Plus most ports do have area's where taxi's will be available to get tourists around and they are worth using if you have never been in an area before but in some cases the transportation costs will be higher. Jamaica itself has a "tourist taxi" called the Juta and it's MUCH more expensive than taking the route taxi (operates similar to a bus service) or the Knutsford Express (intercity bus service) but it has the advantage of being a true point A to point B transport service and often drivers will do work as tour guides.
And a final option is to just hop off the ship and go for a walk. If you don't really know what you want to do and there are no excursions that interest you, go for a walk. The port area's almost always have some sort of duty free shopping and you can easily go outside of the port area and explore. This is also a good option for before or after an excursion because it's basically free. Just be sure to take your passport, a photo ID, and your SeaPass (or whatever you use to get on and off the ship SeaPass is a RCCL naming for it) so that you can get back on the ship and if something happens and you don't make it back in time. I have done this in San Juan - Puerto Rico, Costa Maya - Mexico, Progresso-Mexico, and before an excursion in Georgetown - Cayman Islands. There are a ton of things to look at and sometimes just going into a grocery store can be interesting. For instance in Jamaica you can get all kinds of interesting treats like Rum cake and spice buns among other things. Just make sure that you have an app for doing currency conversion or local currency as most grocery stores are just not setup to handle conversions.
Sooooo I think that's mostly it in a nutshell. The disadvantage of taking an excursion outside of the cruise line offered excursions is you will be less likely to meet some of your other passengers. My first cruise was about 8 months after my wife passed away and I honestly have huge holes in my memory on certain things but a couple years later I lucked upon diving with someone whom I had dove with on that cruise and he remembered me. We got to dive together again and have done our best to stay in touch. If I can ever get some extra cash burning a hole in my pocket he and I are going to head down to Cozumel and spend a week or so diving every chance we can get.
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