Grand Turk: You can purchase an all-day bus pass from the cruiseline but I seem to remember it being ridiculously pricey, to the tune of approximately $35 each.
The bus takes you from the cruisehip terminal to town and some other tourist spots like the lighthouse/museum on the northwest of the island. If I remember correctly, entrance to the lighthouse museum is included in that $35 pass. The island is very small, like 6 miles long by what 1-2 miles wide! Driving on the island is extremely SAFE and a blast!
You just cannot get lost there, no matter how hard you try.
Cruisegal, the driver of the moped has to be 18years of age and hold a valid drivers license, the bikes carry 2 persons easily, William will provide you with crash helmets.
Interesting enough, when we were there in January 2007, he did not even ask for my drivers license, it was a strictly cash deal, no deposit, no nothing! He even let me take the bike for a trial run to make sure I feel comfortable driving it, I tell ya, he's a real pleasant guy. And when you are done, you just return the moped to his location and leave the ignition key in place and just leave! Unheard of here at home!
Guess crime/theft is not an issue for them, there's really nowhere to go with a hot bike!
The south & southwest part of the island there are a few beaches you can stop and swim, snorkel. I carry my own mask, snorkel and fins with me on my cruises. You can buy a good quality set of mask, snorkel & fins for under $20 nowadays, try like BIG 5 sporting goods, Walmart or Kmart, although they may be seasonal items, in that case, order online. Much cheaper than having to rent at each port-of-call.
Nassau, the big draw there nowadays seems to be the Atlantis resort. It is a huge resort with more than just a casino but I think that it is highly over-rated, and that's just my opinion. You can purchase an all-day pass there for around $25 but interestingly enough, that don't give you access to the resort's nice beaches! That will cost you extra. Can you say "TOURIST TRAP". Again, just my opinion. The casino is nice, but living within a 3-hour drive to Las Vegas where we go like 5 times a year, casinos do not impress me or the Mrs anymore! Driving in town is a bit chaotic but once you leave town, it's a breeze. We were there as recently as November 07.
The Straw market, you either love it or you hate it, again, another choatic tourist trap but I think everyone should visit it for that unusual once in a lifetime experience, and once in a lifetime may be way too much!
Again, it is located in town, a few minutes walk from the cruiseship terminal and right next door to Senor Frogs!
A couple of blocks over: another tourist trap: the Pirates Museum, but it may well be worth the visit especially for the kids.
Half Moon Cay, never been there yet!
Hope the above hints help.