In Nassau, we took a taxi into town as well only to find Nassau different from all others; it was not a jewelry mecca. Instead, they had a wonderful mix of a large variety of different stores. The city itself wasn't quite as nice as St. Thomas, but almost, although the streets were much more crowded with vehicles. Make sure you give yourself enough time to get back to the ship (four people were stranded in St. Maarten and had to fly to St. Thomas.)
We took no excursions at any of the ports we stopped at, we are excursioned out from our other cruises and was dropping too much money at the art auctions anyway. At St. Maarten, however, we did hire a van with several others at the taxi stand to take us over to Orient Beach on the French side of the island.
Orient Beach sits on a wide bay on the Northeast side of the island. There are two small and one large islands in the bay itself to add to the beautiful scenery. Even in very early January, the water easy to get into, and I do not like cool water; I keep my pool at 88 degrees when my wife lets me (I recommend heat pumps). The setting where the the van drops you off is very rustic, dirt road rustic with a couple of hutch restaurants and a few stores linings the beach where you can access it.
One warning, if you don't like seeing boobs and other private parts, stick to the middle of the beach. If you travel only a little to the South, you will be in the Orient Nudist Resort which starts with a clothing optional section before getting the full nudity required area. You can, however, travel quite away North before you run into another clothing optional section. If you find a place you want to enjoy the water, you can rent a lounge chair and an umbrella.
As far as activities, I know there is para-sailing, jet skiing, windsurfing and the like, but I am not sure where you go on Orient Bay for those fun things; I just know it wasn't on Orient Beach itself.
For St. Thomas, of the U.S Virgin Islands, we were going to take a tram ride to a high point that overlooks the bay our ship was in until a local told us we could see almost as much from the top of our ship; we went into town instead. If either my wife or I were in the market for jewelry, watches or shoes, we would have been in hog heaven; but, since we weren't, you can guess were we thought we were.
That said, the stores were, for the most part modern, unlike Philipsburg, St. Maarten, and well kept on busy but neat streets. As you walked down the streets you could turn into very interesting "alleys" full of ... you guessed it, shoe, diamond, and watch shops, but each alley had its own atmosphere, which was nice. We were in the market for some sort of native craft and as we walked past one diamond store, the shill asked us to come in for a "special deal". Of course we shook our heads and began to move on when he asked what are we looking for, crafts? To that we stopped and he proceeded to give us directions to a shop further down the street, then into one of the alleys called the International Bazaar, then look for a shop called Tropical Creations. We did, and son-of-a-gun, we found it and it was a craft shop; a very lovely one at that. The artist was the proprietress and we ended up buying one of her works.
While looking at the island from the ship and from the streets, it looked like a pretty island, dotted with obviously nice houses on the hillsides, etc; it was a comfortable looking island, one I might like to come back to for a visit, just not on a cruise. I can only say this of one other island I have visited, the Cayman Islands.