Congradulations on you first cruise. I have been on 15 so I will try to help.
First of all. Pack 12 cans (No Bottles) of your favorite soda in your checked
luggage. No booze allowed. And stay away from those tall glasses like frozen Bahama Mamas. There $7.15 plus tip. For parking use Park-n-go they have good prices and round-trip shuttles or If you park at the Port you are looking at $15.00 a day I think there 8.00 a day or so.
Grand Cayman - First Timers MUST go to Stingray City. It is the best of the tours.
You will love this and you are only in 3 feet of water and if you like you can snorkle with the stingrays. They don't bite and the dont sting. Also Grand Cayman is very Expensive.
Stay away from Hell and the Tuttle Farm- Tourist trap- you can go to both of those places on the local bus for 5 bucks.
Cozumel - Take the ships tour on the Cattamaran. They used to call the tour Snorling and rum punch tour and wow what great rum punch. Keep in mind Cozumel is cheaper downtown than by the ship.
Wear sunscreen even when you do not think you need because trust me you do. Have a great trip. I'm on the Carnval Glory 7 day leaves Dec 5th. Ed