I would research the ports thoroughly. Cruisecritic's message board a have a good Ports of Call subforum with tons of info. Look at the excursions people took. Look at map shows of the areas you're going to.
Not sure where you're going but here are a few of my own thoughts...
In grand cayman if hitting a beach on the 7 mile beach, I'd grab a cab. If going across the island I wouldn't.
On Sint Maarten if just going to the Philipsburg area no excursion needed. If going to St Martin, the French side, I'm still not 100% cool with a cab, but I didn't care for our much touted and loved indepdent tour guide company either (we are one of, like, 3 families who didn't like the tour vs 1000s or even more families who love them, so do NOT take my opinion to heart), so I'm at a loss there.
If I'm St Thomas I would take a cab (big open air bus type things with no seatbelts whatsoever) to a beach. Excursions take you to the same place for more expensive.
You need to know the territory, if cabs are easy, if you're going to a touristy place, etc. Research will give that info.
Oh! If you're going it on your own, make sure someone in your party is wearing a real watch. Not one that pings a satellite and might change to local time. But a good, waterproof, watch. Make sure that's on ship time. Bring the page from the Navigator with you that tells you what time to be onboard. Be onboard at least an hour before that.
That page should also tell you how to contact the port agent if something goes awry.
Reverse engineer your day starting from
when you're getting back onboard. Add in time for each transition. Start your day early. And keep track of that time.
If you're going to Maho Beach in St Martin, know that there's an afternoon traffic jam and a bridge. Make sure you have time for that.
