Welcome to cruise chat! As soon as you get on board, visit the Maitre'd. Normally there will be a table set outside the dining room to solve dining issues on the first day. Let him know your wishes (as well as the fact that you are staying in the Grand Suite). Unless there are extenuating circumstances, you should be accommodated. They may request you dine at your assigned time the first night, but after that they will be able to reseat you. You may also wish to mention your situation to the concierge.
As for the ports you will be visiting. I suggest you check our sister site, PortReviews.com, more specifically www.caribbeanportreviews.com
and click on the link for each of the ports of interest. There is a great deal of information on each of these ports, as well as numerous readers reviews.