Based on our own personal experiences:

Stroller is a must. Preferably your own, or a non-Disney rental, so that you can use it outside of the parks as well.
They need to be able to nap whenever they wish. What you do while they nap, if in the stroller, is up to the adults to negotiate. Chances are the kid(s) will be wiped out for a bit and would sleep through stores, meals, whatever.
We had a lot of fun with all of the no-height-restriction attractions and there are enough of those to keep you busy. Parades/fireworks are the most fun with little ones as well. They love the lights and music.
If they already know particular characters from exposure to Disney movies/cartoons, taking in a character meet/greet with some could be a blast as well. Maybe not so much if they have no idea who the character is, though.