Food - they had plenty of a variety at breakfast and lunch for him to choose for. Dinner they had their own special kids menu with things such as mac n' cheese, spaghetti, chicken strips, French fries, apples, fruit etc. He really enjoyed their French fries more than anything! I think between French fries and Jello he Jwas all set. We did find it easy to get milk for his nightly drink either room service otherwise for breakfast they offered apple juice and at lunch he liked the strawberry kiwi drink (like a crystal light type of drink).
Activities - we did go to the open play group for tots. However, it consisted of a mat with Fisher Price toys on it and that was it. They had farms, tractors, and Little People for them to play with. However, he did enjoy the arcade, swimming/H20 zone, and some shows. The arcade was huge and had everything from skeet ball to car racing to games where claws pick up things. The H20 zone was just as fun as if he was at a water park. The kids splash pool was small, about 3 inches deep, and did have one sprinkler for them to enjoy (this is for those who are not potty trained). The magic show caught his attention with all the lights, tricks, and characters performing. On the Promandae he did enjoy looking at the cows above Ben & Jerrys, the pizza at Sorento's and the Dream Works parades. He even enjoyed ice skating!
Room - they did have a port a crib put up for him that he slept in (some nights); with the curtains drawn it made the room nice and dark for nap time.
Travel - I suggest an umbrella stroller rather than a big one. When you get off in the different ports it makes it easier to be folded and put in a cab, taxi, or shuttle. They try to cram as many people into one so room is limited. Around the ship we didn't use our stroller - he enjoyed walking up/down the stairs, going over the lighted bridge on deck 5, or yes running up/down the hallways.
We did run into a couple that wished they would have brought their 18 month old son when they saw how much fun our son was having. It was a great experience to share with our kids.