My wife and I own a small travel agency and we've been on lots of cruises (21 cruises since 2000) - some suggestions:
At Cozumel if you just want to get loaded check out Paradise Beach:
They have good food, beach side bar, and it's about a 15 to 20 minute taxi ride from port.
Shore excursions - check out independent shore excursions in addition to ones offered by the cruise line. The independent excursions are often just as good if not better, may cost less, and you are with a smaller group. One website we like for independent excursions:
Dining - Your food in the main dining room and the buffet is included in the cost of the cruise. If you want a special romantic dinner for two one night make a reservation at Scarlett's Supper Club. There's an extra charge ($15 or $20 per person) but we thought it was worth it (we ate at Carnival's Supper Club on another ship, the Carnival Liberty, and it was the best meal we had all week, plus we had a table for 2)
Generally the food I've had on my past Carnival cruises has been good. If you don't want to dress up for formal night eating at the buffet in casual clothes is a good option. We usually dress up for one formal night, take pictures, and on the 2nd formal night stay in our shorts and eat at the buffet.
Internet access: many ships do have cell phone access but they also charge INTERNATIONAL ROAMING. I made a call to our sons on from a cruise ship sailing just off of the California coast in February and I was surprised when I got home that it was at the International rate. What I try to do instead is buy an internet package (they'll sell a block of minutes) and keep in touch with people back home by email.
ID's: Very important that you bring the right id to get on the ship. Passports are recommended. For a cruise roundtrip from Miami a driver's license and certified birth certificate is ok, too. You won't get on the ship just with a driver's license.
Have a great time! I am a convert to cruising myself - I never thought I'd like one but gave it a try with my family in 2000. I became hooked, in 2002 became a travel agent, and now I selling cruises is a big part of our business. Our next cruise is on Royal Caribbean's new Oasis of the Seas in November - a huge new ship that will have ziplining, outdoor aquatic theatre, and more - we are excited for that!