First Aid Center
The first aid center at Disneyland is great! I know first hand. The last time we visited the parks our son had a fever. I asked one of the cast members where I could buy children's Tylenol. He directed me to the first aid center where a nurse took his temp and gave me meds for free and my son got a sticker!
Another great place I've used in the past is the Baby Care Center. It is so cute inside! They have changing tables, little potties, high chairs and private rooms for breast feeding! Loved this place when our son was little! They also sell diapers, formula and other baby products.
Disney really thought of everything!