Sorry, none of the attractions (except some of the international pavillions like Mexico) would let us bring in our stroller with the sleeping baby. Even though you can't bring the stroller onto attractions, this can be a great time to just relax in the park, people watch, and baby swap for the bigger rides. In all of the parks there is strolling entertainment in different areas, which you can enjoy with a napping child. Stores are nice as well. They're a little less crowded in the middle of the day.