:wave Hi Tread!
For your first time, I'd recommend going on a ship's excursion. That way, there will be personnel with you to help you get comfortable with your equipment and just snorkeling in general. If you're comfy in the water, it's not difficult to do, but having someone experienced with you can make all the difference. Plus, on a ship's excursion, you're going to go to the better snorkeling locations, where as a general beach can be hit and miss when it comes to what you'll see (sandy areas tend to make for poor snorkeling).
Have you found the list of Princess excursions yet on the Personalizer? It's under Plan Your Voyage. Enter January 9 and select the Dawn Princess and click Search. At the bottom right of the next page is a button entitled "view itinerary" - click that. On the next page the far right column is "Shorex" - click View under that, and you'll be able to view and print out all of the current excursions (subject to change of course, but it gives you an idea).
There is decent to very good snorkeling at each of our stops. Dominica is know for its champagne snorkeling (where natural vents in the ocean floor vent tiny bubbles into the water, making it seem like you're snorkeling in champagne). Barbados has some good areas, Antigua is good, and there are a couple good options on both St. Maarten and St. Thomas/St. John.
What I'd suggest is you take a look at the various islands and excursions offered (either through the ship or independently), see if there is something besides snorkeling you *really* want to do on each, and then opt for snorkeling on the other. I'd also recommend you get with the New Waves staff onboard and ask them for a snorkeling lesson in one of the pools. Since they do full scuba certification onboard, I'm sure there'd be no problem. If there is, I'll teach you
Also, after your first time, you can do it on your own, just making sure you go somewhere that is known for snorkeling rather than simply being a good beach. For example, if we get a group together for the Golden Eagle Catamaran on St. Maarten, that will have great snorkeling as well. I'll be doing that in St. Maarten if we get it together, so you can tag along with me in the water if you like.
I'd be happy to discuss any of this with you! I've been snorkeling since I was 7, and my first dive was at 10, so it's second nature to me. It's a wonderful experience! Let me know how I can help