Plan for Costa Maya to be a beach day. Grab the bus or a taxi into "town" (if that is what they call it) and spend the day at the Cat's Meow for safe food and drinks. Easily done on your own.
Belize - would definately do the cave tubing. If you are uncomfortable doing an independent tour ~ since you are new at this, then take the ship tour.
Grand Cayman ~nice place but very expensive. Again easily done on your own.
I have never been to the last port.
Just remember to take about $50 in one dollar bills to tip the porters ($1 per bag) and to tip room service (which is free 24 hours a day but we do tip $1) and to have some small bills in case you want to "barter to buy something" in Costa Maya or Belize.
Personally, I would not travel past the fence in Belize without an official tour. The locals can be very aggressive and they are having a problem with gangs coming over the border and causing problems. Now you probably would not have a problem, but why have to deal with the stress...you are on vacation!
Costa Maya and Grand Cayman are fine. I don't know about Roatan.