There is a small storage area under the seat and a canopy. The storage area seemed a bit small to me, and the opening is more toward the back, then the top, so I was worried things would fall out.
Depending on the age of your child, you might want to take your own. The Disney ones are jogging type strollers. They have one position- so if you child naps, they have to do it sitting up. If the child is a young baby, I dont think the position and support are the best. Also, hotel location is something to consider. If you are going to be walking back to the hotel with a tired or sleeping child, you'll want your own stroller. We didnt take ours on our last trip. I wont make that mistake again! LOL I already know I"m going to have to fight my hsuband to take it next month, but it will just be so much easier on me and the 4 year old.