Hi tbtest. Welcome.
Belize and G. Cayman have extraordinary waters.
*Grand Cayman--Stingray City is very cool. I would highly recommend swimming with the rays. It's a memory that I will never forget. Very rich port. Beautiful, exclusive shops where the ships' dock....Prada, Versaci, Rolex. The island is well-maintained and clean. If you're just into the beach thing, 7 Mile Beach is the place to head to.
*Belize--I have been to Belize twice. Both times we snorkeled at Goff's Cay. It was beautiful. Reminds me of Gilligan's Island. If/when we go back we will try the cave tubing, only because we've heard it's a great experience.
Downtown Belize is very poor. There is new construction going on and they are trying very hard to earn the American dollar. Sort of a bizarre atmosphere in town. Wandering dogs, a lot of men with snakes draped over their shoulders, who will offer you a photo op with their pet snake. Many locals without limbs, on crutches. I suppose this says a lot about their medical situation in Belize. The locals are very friendly.
Don't shop right at the pier. Walk a bit into their downtown area to experience the real Belize. Here you can do your souvenir shopping. You will find better prices, better selection, and they will barter on goods.
There is also the Belize Zoo if you're into that.
If you're lucky enough, and school is in session, you might be able to see the hundreds of school-age children heading home from school in their uniforms. Strange to see a country, so poor, be so disciplined in their school attire and taking their schooling seriously. It's a great sight.
Have a great cruise.