We always eat at Pancho's Backyard in Cozumel and it is heavenly! It's in the courtyard of Los Cinco Soles (one of the recommended shops that will be on your Cozumel map). The atmosphere, food, and drinks are just wonderful. One of the main reasons we are going on a Western Caribbean next is JUST so we can go back to this fabulous restaurant again.
They claim to have their own in-house purification plant so you don't have to worry about water or ice. We've been fine every time we've eaten there.
FULLY cooked food will be fine almost anywhere as long as it is served right after cooking. Beware of water that is not served in a sealed bottle (ships' water is perfectly safe). Beware of raw foods. Drink beverages prechilled, not in a glass with ice cubes (again not a problem on the ship).
Places where cruise go that would have safe water and food would include Bermuda, Aruba American and British Virgin Islands. Food and water will generally be safe at the MAJOR resorts almost anywhere .
I went to all of the same 4 ports. Brought water (in a sport bottle) with me from the ship. only purchased bottled or canned pop or water. Didn't eat the food, except in Grand Cayman - went to KFC for a quick bite. the food was fine but I ordered a large coke - of course, it was a fountain pop with ice. I never gave it a second thought, but later that night and for the next 2 days, I was definitely feeling "wonky." had to lie down for a while that night, and could only eat a bit of cheese and fruit (the waiter was excellent - had the chef prepare something lite like that for two nights). Had stomach pains for two days, and that was the only time I felt the motion of the boat (while I was already sick). My advice would be to definitely avoid the water everywhere except the ship. in terms of food, you'd probably be ok but remeber that the vegetables and fruit are likely washed and perhaps cooked in the water. If you order room service sandwcih the morinig of a port day, you can take the sandwich with you to eat on the go. saves money too. just my thoughts.
Your food is included on the ship. We just occationally grab a snack. Grand Cayman does have very good food. In all ports in the Caribbean: No not drink the water. Remember no ice cubes either. Also, no uncooked fruit or veggies.
Just be aware while in Mexico....Don't get drinks with ice (soda, frozen drinks, etc...).
While in Costa Maya we got drinks in cans (coke) and they brought us glasses with ice...we didn't use the ice...we drank right out of the soda can. Better to be safe then sorry but you know most of those restuarants do use filtered water.