Hi 03bowtie, welcome to CruiseReviews
Eastern could be St. Thomas, St. Maarten, or a whole bunch more. So I'll go with St. Thomas and St. Maarten. If you want to stay on the island of St. Thomas, Coki Beach and Megan's Bay are the best beaches for ammenities. Sapphire Beach is better for snorkeling, but has a lot of little rocks on the shoreline and not as many ammenities. If you don't mind taking a little trip, Trunk Bay on St. John is totally amazing. You can catch the ferry in Red Hook and Charolette Amalie. Red Hook has a better schedule, though, more reliable. Then you grab a cab and go to Trunk Bay. It used to be about $4/ea. for entrace, but that may have gone up.
St. Maarten, most everyone goes to Orient Beach. It is clothing optional and most of the ones that go for the nonclothed option, shouldn't. Another beach is Maho and that's where the planes seem to land on top of you. The last time we were there, we did an excursion through the ship to the TikiHut. It was a floating dock with drinks/food available, decent snorkeling, and run by a great crew. They'd take you back to town for shopping or back to the ship, whenever you wanted. No set time limits. Of course, you have to be back 1/2 hour before sailing.
I'll second the Fish 'n Chips, it's great. And don't forget to try the chocolate melting cake---mmmmmmmmmmmmmm good!