tailgating HOF,
I have cruised Carnival 3 times -- once out of Miami (Ecstasy) and twice out of Galveston (Conquest, Magic).
regarding Cozumel, try the Twister boat to Isla Pasion. Very nice beach, I think it's the one where they film those Corona commercials (couple sitting on the beach, squirt limes -- you know the ones). The twister boat takes on about a 20 minute ride to the island... once on the island they have a few free activities (kayakes, paddleboats, water trampoline), and pretty nice buffet as well.
https://www.carnival.com/shore-excursions/cozumel/all-inclusive-isla-pasion-by-twister-304107I would get on the ship as early as you can since it's your first cruise, gives you time to walk around and explore for a while, get your bearings, get some food, etc.
I would suggest bringing on a case of soft drinks or water bottles.
Also bring a large mug with a lid or something like that if you plan on eating outside, buffet,etc (non-main dining room)... the cups they give you are tiny and you will waste a lot of time (and energy) walking back and forth to get refills of iced tea, water, lemonade and their drink stations.
Don't spend much time in your cabin,,, you can hang out in a "hotel room" another time. Wake up early, stay up late. Go out and see every show (magic shows, dance show, stand-up comeding-- catch the PG13 version during the evening and the "Adult" version after 10pm), explore the ship, chill on the side decks of the ship if you want "quiet time". Go to at least a couple of breakfasts and dinners at the main dinning room, order foods you have never tried before, order two entrees at dinner.
If you have any specific questions, feel free to ask here.