First, the getting on and off the boat topic. I have been on 11 (I think) cruises now and never experienced a port that you were herded off and not allowed to return until the end of the day. I've had it suggested before because the cruise ship anchors in the harbor and you have to tender (water taxi) back and forth to the ship and it is not real convenient, but if you have 8 hours it shouldn't be a problem. Grand Cayman you will anchor and water taxi. Most ships will have a tender ticket type of scheme to get off first thing in the morning. If you read this in your nightly cruise newspaper of events. Get to this line early to get one of the first tenders off and you'll be all set. It's a lot like getting a Now Serving # at the Deli counter. Cozumel you will definately be at the pier and can come and go as much as you please. Montego Bay should be similar, but I'm not sure how Hurricane Ivan left them so be prepared for either scenario.
If you have never been diving in Cozumel, definately do it. It is fine to do it through the ship (since it is your first cruise). There are tons of dive operators there so I have never been overcrowded on the dive charter. Diving in Cozumel is drift diving and very beautiful coral and tons of sealife. After your dive you should have plenty of time to go back to the ship, dump your wet gear, quick shower and on to the streets. Rinse your stuff later (other than reg. setup) when you're done for the day to get the most out of each port. There is tons of shopping in Cozumel all walking distance from the pier. If either of you like silver jewelry, etc. bring some extra $$. If you are drinkers, alcohol on the the cruiseship is expensive. If you like Corona - they might be $1 on the main tourist street, go 1 block inland they're 2 for $1, and go and extra block they're 3 for a $1. The same goes for t-shirts and any other similar souvenier. The cruise ship will hand you a shopping map with "suggested stores" for each port the night before you arrive or on the gangplank.
Grand Cayman, also great diving, but here to see the most of Grand Cayman most ships offer some good combo tours - like Stingray City and Cayman Tour where they will take you to the town of Hell, the turtle farm, seven mile beach etc. Some of them are snorkelling tours, some are land-based. You'll have to read the descriptions and pick the one that suits you best. If you want to do some cheap shore diving instead look up Eden Rock on the web. It's a 5-10 min walk from where the water taxi drops you off and my husband and I dove in a very relaxed atmosphere. 4 tanks and weights came to about $40, then we wheeled our bag of gear into the tourist streets to grab some lunch and did a little shopping before heading back to the boat. Either choice here - tour or shore diving - you won't be disappointed.
Montego Bay, again, I'm not sure what is left after Ivan. Don't expect to do any diving here. The biggest tourist trap is probably walking up Dunn's River Falls. I've done it and was not disappointed, but if I were to do it on my honeymoon (especially after the destruction on towns - thanks, Ivan) I might try getting out into the countryside a bit on one of the tubing tours the cruises typically offer.
I've hope my experiences help you. If you are not the adventurous types I can suggest stuff that might be a little more laid back but just as enjoyable. Carnival has their shore excursions descriptions online. My suggestion is to read through them. The first thing to do once you get to your room on the boat, is check your newsletter, see when the shore excursion desk is open and book your excursions as quickly as possible. DON'T WAIT until the second day as a lot of the favorites tend to fill up. It doesn't appear that Carnival allows you to pre-register for the tours before you reach the boat. So book early and explore the boat after. You'll be on the boat for a week.
Oh, one more thing. Don't bring the lead with you! All scuba tours include tanks and weights. Some include the gear, but I know in Cozumel they make you rent it for approx. $15 per major component. Taking your own gear although bulky at times gives you peace of mind.
Any other questions? Don't be afraid to ask. It should be a great experience for you.
Hope you have as much of a blast as we did on our last cruise.
