We happened upon a seaside restaurant/bar called the "No Name Beach Club" just a short walk from the main cruise terminal on our first cruise, so we made it a point to return for drinks and lunch. Apparently, this is also a popular spot for the ship crews, as part of the No Name's slogan is "For crew, by crew." This was proven to be the case, as we saw several of our own ship's crew drop by in their "civilian" clothes.
Souvenirs are plentiful, and with just a little comparative shopping, one can make many purchases without spending too much money.
There were two other cruise ships there, from Holland America Line and Royal Caribbean, but even with three large cruise ships visiting at the same time, the cruise terminal area didn't seem that crowded.
We didn't take any specific excursion, but rather enjoyed some souvenir shopping and geocaching in the area. Jimmy Buffett's Margaritaville restaurant, while a bit pricey, was a fun place for lunch.
I was first exposed to Del Sol's products during an Alaskan cruise last year. These shirts, caps, and even nail polish, change colors in sunlight. We found a Del Sol shop nearby and purchased several Grand Cayman specific shirts. I highly recommend any of these Del Sol products.
Appleton Estate Rum is manufactured exclusively in Jamaica, according to the tour guide, so it was a very fascinating tour to take. The ride from the cruise terminal to the Plantation was approximately 2 1/2 hours each way. Several of our group compared this ride to a roller coaster ride, in that there were many hair pin turns, and multiple "ups and downs" along the way. We traveled in a caravan of about 5 vans, and had a police escort there and back.
The tour itself started with a visit to the visitor's center for complimentary rum punch. A sample of raw sugar cane was also offered. The actual tour included a visit to the distillery as well as the ageing room and a display of older processing techniques. Lunch and a rum tasting session completed the tour.
Other than this excursion, we did not tour any other part of Montego Bay.