The baby care building is located in the kid's area right across from the Shamu stadium.
Another baby care area that was really unexpected but great was at Aquatica. They have their nursing room right next to the kids area. It is a small nursing room but it was perfect for a water park.
Disney World also has a good nursing room. The few times I used it though it was packed It was a lightly lit room with rocking chairs and lots of nursing mamas. To tell you the honest truth when I go to Disney I don't personally use it. I normally just sit down and nurse with a coverup. Especially since there is only one nursing area and it is located on Main Street. It is far too inconvenient in the park to find your way back to the nursing room every time you need it.
It is great to always have a comfortable air conditioned stop for you and your little one.