Long Time, I've been on many cruises to Mexico and the Caribbean. If your not familiar with going to foreign countries, than I suggest you use the tours and excursions from the ship. I suggest this for several reasons. 1. SAFETY..On a ship excursion,they are responsible for you and the ship will not leave port without you. If you go out on your own and are not back by the time the ship leaves...your stuck like chuck!! 2.In all ports, there are plenty of hustlers just waiting to take advantage of the unsuspecting traveler. I've seen it happen a bunch of times. Get in the wrong cab and before you know it your having a very bad day! 3. The ship tours and excursion are a little pricey but they are reputable AND you still get to see the area. A van or bus meets you at the ship, takes you to where you chose and brings you back. It's just a safer way to LEARN about other countries. At least for your first cruise,this is my suggestion for you.
I go out on my own all the time, I very rarely go on a ship excursion,but, I been on 20+ cruises , to every island in the Caribbean and I have experienced what to do and what not to do. Whatever you decide, be careful and have a Great Cruise.